Priority Queue

This paper analyzes Markovian queuing system wherein the arrival process remains in two states i.e., active state and passive state with arrival rate  and 0 respectively. When the input enters in the passive state; service rate remains same as in active state, for a random time K with exponential distribution having parameter i  . After random time K , the input is still in passive state, the service rate changes to j  till the input shifts to active state, when the input shifts to active state the service rate becomes i  . When the service rate is i  and the duration of time for which the input is in passive state is less than K ; this state is known as passive state phase I. When the service rate is j  , and the duration of time for which the input remains passive is larger than K ; this state is called as passive state phase II. Laplace transforms of the various probability generating functions are obtained and the steady state results are explicitly derived. Variance and expected number of units in the system are also analyzed.

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Ranked subsequence matching finds top-k subsequences most similar to a given query sequence from data sequences. Recently, Han et al. [12] proposed a solution (referred to here as HLMJ) to this problem by using the concept of the minimum distance matching window pair (MDMWP) and a global priority queue. By using the concept of MDMWP, HLMJ can prune many unnecessary accesses to data subsequences using a lower bound distance. However, we notice that HLMJ may incur serious performance overhead for important types of queries. In this paper, we propose a novel systematic framework to solve this problem by viewing ranked subsequence matching as ranked union. Specifically, we propose a notion of the matching subsequence equivalence class (MSEQ) and a novel lower bound called the MSEQ-distance. To completely eliminate the performance problem of HLMJ, we also propose a costaware density-based scheduling technique, where we consider both the density and cost of the priority queue. Extensive experimental results with many real datasets show that the proposed algorithm outperforms HLMJ and the adapted PSM , a state-of-the-art index-based merge algorithm supporting non-monotonic distance functions, by up to two to three orders of magnitude, respectively.

This paper analyses preemptive and non preemptive opportunistic spectrum access of secondary user in cognitive radio network (CRN) using M/D/1 analytical queuing model. Secondary users opportunistically access the spectrum of primary user if the channel is free. For preemptive priority high priority packet preempt a low priority packet and for non preemptive a high priority packet does not preempt a low priority packet instead it waits at head of line (HOL) until channel becomes free. Preempting a Secondary packet and not preempting a secondary packet has effect on packet waiting time and revenue collected from SUs for spectrum sharing. Through spectrum sharing spectrum owner tries to generate more revenue whereas SUs tries to maximize their satisfaction. Numerical illustration is presented using utility function to determine upper and lower boundary of primary arrivals for both preemptive and non preemptive. By using boundaries Optimal secondary packet arrival rates are derived .Analytical results demonstrate that the preemptive priority allow many Secondary packets to be transmitted in short time and in case of non preemptive priority the transmitting secondary packet uses short time but transmitting probability of secondary packet waiting in queue to get a channel becomes very low.

This paper analyses preemptive and non preemptive opportunistic spectrum access of secondary user in cognitive radio network (CRN) using M/D/1 analytical queuing model. Secondary users opportunistically access the spectrum of primary user if the channel is free. For preemptive priority high priority packet preempt a low priority packet and for non preemptive a high priority packet does not preempt a low priority packet instead it waits at head of line (HOL) until channel becomes free. Preempting a Secondary packet and not preempting a secondary packet has effect on packet waiting time and revenue collected from SUs for spectrum sharing. Through spectrum sharing spectrum owner tries to generate more revenue whereas SUs tries to maximize their satisfaction. Numerical illustration is presented using utility function to determine upper and lower boundary of primary arrivals for both preemptive and non preemptive. By using boundaries Optimal secondary packet arrival rates are derived .An...

The Internet of Things (IoT) protocols have encountered great challenges as the growth of technology has led to many limitations of the performance of the IoT protocols. Message Queuing Telemetry Transport protocol (MQTT) is one of the most dominant protocols in most fields of smart applications, so it has been chosen in this research to be a use case for implementing and evaluating a new proposed Back-off algorithm that is designed to eliminate suspicious and fake messages by calculating an initial frequent rate for each publisher connected to the MQTT broker. The proposed Backoff algorithm was designed to mitigate the traffic load of the uplink traffic by applying an exponential delay factor to suspicious publishers. Another priority scheduling algorithm was proposed to classify publishers as high priority or low priority depending on the new calculated frequent rate. The two algorithms were implemented on the Mosquitto broker and evaluated using a simulation environment by measuring specified performance metrics. The simulated results proved that the Back-off algorithm eliminated network load and introduced an acceptable range of CPU and RAM consumption. The results also concluded that the priority classification algorithm managed to reduce the latency of high-priority publishers.

The Internet of Things (IoT) protocols have encountered great challenges as the growth of technology has led to many limitations of the performance of the IoT protocols. Message Queuing Telemetry Transport protocol (MQTT) is one of the most dominant protocols in most fields of smart applications, so it has been chosen in this research to be a use case for implementing and evaluating a new proposed Back-off algorithm that is designed to eliminate suspicious and fake messages by calculating an initial frequent rate for each publisher connected to the MQTT broker. The proposed Backoff algorithm was designed to mitigate the traffic load of the uplink traffic by applying an exponential delay factor to suspicious publishers. Another priority scheduling algorithm was proposed to classify publishers as high priority or low priority depending on the new calculated frequent rate. The two algorithms were implemented on the Mosquitto broker and evaluated using a simulation environment by measuring specified performance metrics. The simulated results proved that the Back-off algorithm eliminated network load and introduced an acceptable range of CPU and RAM consumption. The results also concluded that the priority classification algorithm managed to reduce the latency of high-priority publishers.

Customers are compelled to queue when a service system is at its busiest. This issue not only reduces customer pleasure, but it also causes the company to lose money. For consumer losses, this study proposes a queue model of customer queuing behavior. The goal is to reduce customer losses, hence researchers are looking at queue setup and optimization in random service systems. We developed three queuing models: MG1, GM1, and GG1 for estimating service quality control. We investigate queuing systems for predicting replies for service quality control based on queue models of customer behavior. The study found that the MG1 queue model yields the best service quality, however the GM1 and GG1 results are relatively close behind.

To integrate the Fifth Generation (5G) Vehicular ad hoc network (VANET) based clustering in cellular networks is useful for improving the throughput, saving scarce spectrum resources and preventing network congestion, as well as reducing the packet loss. However, it is a challenging problem to find an optimized clustering algorithm that has efficient stability adapting to dynamic VANETs. Considering the advantages of software-defined networking (SDN), an the 5G VANET system is employed with an SDN-enabled social-aware adaptive clustering algorithm (SESAC) which exploits a social pattern (i.e., future route) of every vehicle to optimize the stability of each cluster. To design the homogeneous Semi-Markov model for discrete time, which is based on the movement of each vehicle. The state transition probability and exact time probability dissemination are inputs while social patterns of each vehicle's are output. The anticipated social patterns are generally used to make groups(cluster); where the vehicles are in a similar cluster, the cluster head (CH) will share a similar way (similar route). The cluster heads (CHs) are selected by some specific metrics such as inter vehicle distance, relative speed, and attributes of vehicle. Finally the SESAC algorithm is analyzed and compared with the conventional clustering algorithm.

In a multi-tasking system a writer task generates real-time and non real-time messages having multiple priority levels in an ascending order arranged in a plurality of priority bands. The real-time messages have predetermined timing deadlines. A plurality of queues indexing the messages by pointers, there is one queue for each priority band. A dispatcher moves pointers from a lower priority queue to a higher priority queue in response to a time-out signal dependent on the timing deadline. A data push agent transmits the messages indexed by the pointers according to the multiple priority levels.

In this paper, we show how to improve the complexity of heap operations and heapsort using extra bits. We first study the parallel complexity of implementing priority queue operations on a heap. The trade-off between the number of extra bits used, the number of processors available, and the parallel time complexity is derived. While inserting a new element into a heap in parallel can be done as fast as parallel searching in a sorted list, we show how to delete the smallest element from a heap in constant time with a sublinear number of processors, and in sublogarithmic time with a sublogarithmic number of processors. The models of parallel computation used are the CREW PRAM and the CRCW PRAM. Our results improve those of previously known algorithms. Moreover, we study a variant, the fine-heap, of the traditional heap structure. A fast algorithm for constructing this new data structure is designed using an interesting technique, which is also used to develop an improved heapsort algorithm. Our variation of heapsort is faster than Wegener's heapsort and requires less extra space.

This paper proposes a novel scheduling discipline for service differentiation among traf®c classes in multi-service networks, which is referred to as the Probabilistic Priority (PP) discipline. The PP discipline is based on the Strict Priority (SP) discipline with the difference that each priority queue is assigned a parameter as in Weighted Fair Queueing (WFQ) and Weighted Round Robin (WRR) disciplines. The parameter determines the probability with which its corresponding queue is served when it is polled by the server. Similar to WFQ and WRR, service differentiation as well as fairness among traf®c classes can be achieved in PP by setting the assigned parameters properly. In addition, the PP discipline can be easily reduced to the ordinary SP discipline or to the reverse SP discipline. Moreover, the PP discipline can provide service segregation among groups of traf®c classes while at the same time provide service differentiation among classes within each group. The proposed PP discipline may be used in controlling per-hop behavior in differentiated services networks.

We present a comprehensive review of the discrete Boussinesq equations based on their three-component forms on an elementary quadrilateral. These equations were originally found by Nijhoff et al using the direct linearization method and later generalized by Hietarinta using a search method based on multidimensional consistency. We derive from these three-component equations their two-and onecomponent variants. From the one-component form we derive two different semicontinuous limits as well as their fully continuous limits, which turn out to be PDE's for the regular, modified and Schwarzian Boussinesq equations. Several kinds of Lax pairs are also provided. Finally we give their Hirota bilinear forms and multi-soliton solutions in terms of Casoratians.

Lifetime of node-to-node communication in a wireless ad hoc network is defined as the duration that two nodes can communicate with each other. Failure of the two nodes or failure of the last available route between them ends their communication. In this paper, we analyze the maximum lifetime of node-to-node communication in static ad hoc networks when alternative routes that keep the two nodes connected to each other are node-disjoint. We target ad hoc networks with random topology modeled as a random geometric graph. The analysis is provided for (1) networks that support automatic repeat request (ARQ) at the medium access control level and (2) networks that do not support ARQ. On the basis of this analysis, we propose numerical algorithms to predict at each moment of network operation, the maximum duration that two nodes can still communicate with each other. Then, we derive a closed-form expression for the expected value of maximum node-tonode communication lifetime in the network. As a byproduct of our analysis, we also derive upper and lower bounds on the lifetime of node-disjoint routes in static ad hoc networks. We verify the accuracy of our analysis using extensive simulation studies.

The queueing theory is applied to analyse a model of a multiprogramming operating system in which preemptive priorities are used for scheduling the service of concurrent streams of requests. Preemptions are permitted at the end of each service quantum. Mean waiting times and higher statistical moments in the M/G/1 system analysed are computed.

The queueing theory is applied to analyse a model of a multiprogramming operating system in which preemptive priorities are used for scheduling the service of concurrent streams of requests. Preemptions are permitted at the end of each service quantum. Mean waiting times and higher statistical moments in the M/G/1 system analysed are computed.

We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer's class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements

We present several simple probabilistic data structures for implementing priority queues. We present a data structure called simple bottom-up sampled heap (SBSH), supporting insert in O(1) expected time and delete, delete minimum, decrease key and meld in O(log n) time with high probability. An extension of SBSH called BSH1, supporting insert and meld in O(1) worst case time is presented. This data structure uses a novel "buffering technique" to improve the expected bounds to worst-case bounds. Another extension of SBSH called BSH2, performing insert, decrease key and meld in O(1) amortized expected time and delete and delete minimum in O(log n) time with high probability is also presented. The amortized performance of this data structure is comparable to that of Fibonacci heaps (in probabilistic terms). Moreover, unlike Fibonacci heaps, each operation takes O(log n) time with high probability, making the data structure suitable for real-time applications.

In [2], a steepest descent algorithm, which minimises the output signal energy E(y,*(i]}, was used for controlling the weights. The weights that achieve this are obtained by an iterative search: That is, the algorithm, by minimising the output energy, forces the correlation between the desired output signal and vector of tentative decisions of interfering signals to zero. In a practical implementation, the expected value j n eqn. 3 would be replaced by its instantaneous realisation y,(i)b ,(Q. Therefore, the weight update equation becomes For the RLS-type, choose at time i the weight vector w,'(i] that minimises X,=; h'Jy,*(j), where h is called the forgetting factor and 0 < h < I, i.e. The solution of the above equation is where R(i) = c X 2 -3 b l ( j ) b T ( j ) and d ( i ) = ~X z -J 6 1 ( j ) z l ( j ) J=O J=O R(i) and d(i) follow the recursive equations R(i + 1 ) = XR(i) + bl(i + l ) b Y ( i + 1 ) d ( i + 1) = Xd(i) + b,(i + l).l(i + 1 )

We introduce a probabilistic version of the iterated factor method introduced in our previous investigations. Let $n$ be drawn uniformly from $\{1,2,\ldots,M\}$. Set $$s:=s(n)=\left \lfloor \frac{\sqrt{\log_2n}}{\log \log_2n} \right\rfloor \quad \textbf{and} \quad t(n)=\sqrt{\log \log n}$$ and $$k_n=\left \lfloor \frac{n}{2}\right \rfloor_s.$$ Then as $N\longrightarrow \infty$ with $Z_n\sim N(0,1)$~(normally distributed) and additionally that $$\mathrm{Pr}[\nu(k_n)\leq s \quad \mathbf{and} \quad |Z_n|\leq t]\longrightarrow 1$$ we show that inequality $$\iota(2^n-1)\leq n-1+\log_2n+C\sqrt{\frac{\log_2n}{\log \log_2n}}$$ for some absolute constant $C>0$. This breaks the $O(\frac{\log n}{\log \log n})$ barrier that is guaranteed to be achieved using the Brauer method \cite{brauer1939addition}. This result can be seen as injecting probabilistic methods into the theory of addition chains.

In this paper, we present a fast and scalable pipelined priority queue architecture for use in high-performance switches with support for fine-grained quality of service (QoS) guarantees. Priority queues are used to implement highest-priority-first scheduling policies. Our hardware architecture is based on a new data structure called a Pipelined heap, or P-heap for short. This data structure enables the pipelining of the enqueue and dequeue operations, thereby allowing these operations to execute in essentially constant time. In addition to being very fast, the architecture also scales very well to a large number of priority levels and to large queue sizes. We give a detailed description of this new data structure, the associated algorithms and the corresponding hardware implementation. We have implemented this new architecture using a 0.35 micron CMOS technology. Our current implementation can support 10 Gb/s connections with over 4 billion priority levels .

We consider, as in part I (see above), a random walk X t ∈ℤ ν , t∈ℤ + , and a dynamical random field ξ t (x), x∈ℤ ν , in mutual interaction with each other. The model is a perturbation of an unperturbed model in which walk and field evolve independently. Here we consider the environment process in a frame of reference that moves with the walk, i.e., the “field from the point of view of the particle” η t (·)=ξ t (X t +·). We prove that its distribution tends, as t→∞, to a limiting distribution μ, which is absolutely continuous with respect to the unperturbed equilibrium distribution. We also prove that, for ν≥3, the time correlations of the field η t decay as const·e -αt /t ν/2 .

The present study deals with the double orbit finite capacity retrial queues with unreliable server. The system facilitates the arrival of two types of customers known as priority and non priority customers and can hold a maximum of L priority customers and K non-priority customers as per its capacity. The priority customers are served prior to the non-priority customers. Moreover, the server is unreliable which may breakdown while servicing either priority or non-priority customer. The failed server is sent for repair following threshold recovery policy to become as good as earlier. Both transient as well as steady state analysis of the model has been done using by matrix method. Various performance measures including queue length, reliability metrics, long run probabilities, etc. have been obtained using various state probabilities. The application of the model to cellular radio network has been discussed. The cost function has been constructed and optimized using meta heuristic approach. The sensitivity analysis of various performance indices has been performed as an illustration.

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on-off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in This work has been carried out partly in the Dutch BSIK/BRICKS project.

Data backup processes are power intensive jobs and use substantial server resources. While serving each data packet immediately on arrival would result in too many connections to the cloud server, data packets, on the other hand, cannot be kept waiting in the buffer for too long. Power spent to keep the server on can be optimized by forcing the server to take a vacation when there are no packets to backup. Further, the number of new connections to the cloud server can be reduced by backing up batches of packets. Therefore, we introduce a new queueing model which has a single batch server and employs an exhaustive service discipline. As soon as the backlog of the server becomes zero, the system enters a vacation. During a vacation, the server consumes minimal power while the data packets arrive and wait in a buffer for backup service. When the server wakes up from the vacation, the server starts serving a batch, that is a new backup is initiated, if some starting conditions are met, otherwise it enters a new vacation period. These starting conditions depend on the number of backlogged packets. If at least l packets (starting threshold of policy) are present in the queue, the system resumes service. If there are i packets in the queue, where i is less than l, the service resumes with probability α i or another vacation period starts with probability (1 -α i ). Such probabilistic starting conditions lead to shorter waiting time of data packets in comparison to fixed threshold based conditions. The service time of a batch is dependent on the number of packets in that batch. We analyze the performance of this queueing model and present how it can provide the same Quality of Service of data backup as existing queueing models at a cheaper cost. This can be achieved either by using a cost effective backup server or by ensuring that the system takes longer vacations.

In many studies on batch service queueing systems, the service capacity is assumed to be constant. However, this service capacity often depends on the content of the queue. In this paper, we analyse a discrete-time single server batch server queue with general independent arrivals. We distinguish two different classes in the arrival stream and products of both classes are added to the tail of a single queue. The single batch server can group all waiting customers at the head of the queue that belong to the same product class up to a certain class-dependent maximum capacity. This results in a stochastic service capacity that depends on both the number of customers in the queue and their respective classes. Since it is clear that the length of a sequence of same-class customers will have a significant impact on the performance of the system, we also include correlation between the classes of consecutive customers. Applications of this type of batch server can, for instance, be found in the pacemaker loop of a Lean manufacturing system. In the course of the analysis, we calculate the probability generating function of the system occupancy at service initiation opportunities. In the numerical experiments, we will look at the impact of different parameters on both the mean system occupancy and the probability that the server is idle at a random service initiation opportunity. We also provide a number of guidelines to pick between the exact solution and an approximated approach with unlimited service capacities, by looking at the trade-off between accuracy and computational complexity.

Existing concurrent priority queues do not allow to update the priority of an element after its insertion. As a result, algorithms that need this functionality, such as Dijkstra&#39;s single source shortest path algorithm, resort to cumbersome and inefficient workarounds. We report on a heap-based concurrent priority queue which allows to change the priority of an element after its insertion. We show that the enriched interface allows to express Dijkstra&#39;s algorithm in a more natural way, and that its implementation, using our concurrent priority queue, outperform existing algorithms. A priority queue data structure maintains a collection (multiset) of items which are ordered according to a priority associated with each item. Priority queues are amongst the most useful data structures in practice, and can be found in a variety of applications ranging from graph algorithms [21, 5] to discrete event simulation [8] and modern SAT solvers [4]. The importance of priority queues has m...

Existing concurrent priority queues do not allow to update the priority of an element after its insertion. As a result, algorithms that need this functionality, such as Dijkstra&#39;s single source shortest path algorithm, resort to cumbersome and inefficient workarounds. We report on a heap-based concurrent priority queue which allows to change the priority of an element after its insertion. We show that the enriched interface allows to express Dijkstra&#39;s algorithm in a more natural way, and that its implementation, using our concurrent priority queue, outperform existing algorithms.

IEEE 802.16 standard provides resources to both service classes Constant Bit Rate (CBR) and Variable Bit Rate (VBR). These services require enough resources to transmit data efficiently. In this paper, a Service Based Fair Resource Allocation (SBFRA) Mechanism is proposed, for assessing the required service from Subscriber (SS) along with the channel condition. The proposed model evaluates the required additional resources in order to provide the required service to SS. In this proposed model, a Priority Queue Scheduling Methodology is presented in order to provide additional resources as per channel condition. A comparison is made with and without the proposed model on both traffic, CBR and VBR. The experiments show that the proposed design manages the user request by providing them additional resources as per requirement. The requestsare handled in Priority Queue Scheduling based mechanism. Results show that an improvement is achieved by providing the additional resource on fair scheduling basis. To achieve the required performance for fairness there is a compromise on delay.

This paper introduces a rather general technique for computing the average-case performance of dynamic data structures, subjected to arbitrary sequences of insert, delete, and search operations. The method allows us effectively to evaluate the integrated cost of various interesting data structure implementations, for stacks, dictionaries, symbol tables, priority queues, and linear lists; it can thus be used as a basis for measuring the efficiency of each proposed implementation. For each data type, a specific continued fraction and a family of orthogonal polynomials are associated with sequences of operations: Tchebycheff for stacks, Laguerre for dictionaries, Charlier for symbol tables, Hermite for priority queues, and Meixner for linear lists. Our main result is an explicit expression, for each of the above data types, of the generating function for integrated costs, as a linear integral transform of the generating functions for individual operation costs. We use the result to compute explicitly integrated costs of various implementations of dictionaries and priority queues.

The paper investigates the machine repair problem consisting of M operating machines with S spare machine and R servers where machines have two failure modes and server are subjected to breakdown under steady state conditions. The two failure modes have equal probability of repair. Spares are considered to be cold standby or warm standby or hot standby. Failure and service time of machines and breakdown and repair time of server are assumed to follow a negative exponential distribution. Each server is subject to breakdown even if no failed machine is in the system.

A number of nonlinear programming algorithms are proposed to obtain the approximate solutions for nonproduct form multiclass queueing network models, as well as priority queueing networks. Using sensitivity analysis, we develop an efficient iterative technique for closed queueing networks. We compare the approximate solutions obtained from our approach with the global balance solution. Examples illustrate the accuracy of the approximation, and compare the efficiency of the different optimization methods we have implemented.

We derive a revenue-maximizing scheme that charges customers who are homogeneous with respect to their waiting cost parameter for a random fee in order to become premium customers. This scheme incentivizes all customers to purchase priority, each at his/her drawn price. We also design a revenue-maximizing scheme for the case where customers are heterogeneous with respect to their waiting cost parameter. Now lower cost parameter customers are encouraged to join the premium class at a low price: Given that, those with high cost parameter would be willing to pay even more for this privilege.

We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.

We derive a revenue-maximizing scheme that charges customers who are homogeneous with respect to their waiting cost parameter for a random fee in order to become premium customers. This scheme incentivizes all customers to purchase priority, each at his/her drawn price. We also design a revenue-maximizing scheme for the case where customers are heterogeneous with respect to their waiting cost parameter. Now lower cost parameter customers are encouraged to join the premium class at a low price: Given that, those with high cost parameter would be willing to pay even more for this privilege.

A model of human visual perception of collisions is presented, based on twodimensional measures of eccentricity and separation. The model is validated by performing psychophysical experiments. We demonstrate the feasibility of using this model as the basis for perceptual scheduling of interruptible collision detection in a realtime animation of large numbers of visually homogeneous objects. The user's point of fixation may be either tracked or estimated. By using a priority queue scheduling algorithm, perceived collision inaccuracy was approximately halved. The ideas presented are applicable to other tasks where the processing of fine detail leads to a computational bottleneck.

Previously, it was shown in a paper by Kaldewaij and Schoenmakers that for topdown skew heaps the amortized number of comparisons required for meld and delmin is upper bounded by log φ n, where n is the total size of the inputs to these operations and φ = ( √ 5 + 1)/2 denotes the golden ratio. In this paper we present worst-case sequences of operations on top-down skew heaps in which each application of meld and delmin requires approximately log φ n comparisons. As the remaining heap operations require no comparisons, it then follows that the set of bounds is tight. The result relies on a particular class of self-recreating binary trees, which is related to a sequence known as Hofstadter's G-sequence.

The problem of solving large Markov decision processes accurately and quickly is challenging. Since the computational effort incurred is considerable, current research focuses on finding superior acceleration techniques. For instance, the convergence properties of current solution methods depend, to a great extent, on the order of backup operations. On one hand, algorithms such as topological sorting are able to find good orderings but their overhead is usually high. On the other hand, shortest path methods, such as Dijkstra's algorithm which is based on priority queues, have been applied successfully to the solution of deterministic shortest-path Markov decision processes. Here, we propose an improved value iteration algorithm based on Dijkstra's algorithm for solving shortest path Markov decision processes. The experimental results on a stochastic shortest-path problem show the feasibility of our approach.

In this paper we study the problem of scheduling variable-length frames in WDM-PON under Stanford University aCCESS (SUCCESS), a next-generation hybrid WDM/TDM optical access network architecture. The SUCCESS WDM-PON architecture has unique features that have direct impact on the design of scheduling algorithms: First, tunable transmitters and receivers at OLT are shared by ONUs to reduce transceiver counts; Second, the tunable transmitters not only generate downstream data traffic but also provide ONUs with optical Continuous Wave (CW) bursts for upstream transmissions. To provide efficient bidirectional transmissions between OLT and ONUs, we propose a batch scheduling algorithm based on the sequential scheduling algorithm previously studied. The key idea is to provide room for optimization and priority queueing by scheduling over more than one frame. In the batch scheduling, frames arrived at OLT during a batch period are stored in Virtual Output Queues (VOQs) and scheduled at the end of the batch period. Through simulation with various configurations, we demonstrate that the proposed batch scheduling algorithm, compared to the original sequential scheduling algorithm, provides higher throughput, especially when the system load is high, and better fairness between up-and downstream transmissions. CHEDULING variable-length messages under the constraints of shared resources is critical for the success of advanced, next-generation wavelength-routed optical networks where tunable transmitters and tunable or fixed receivers are shared by many users in order to reduce the high cost of Wavelength Division Multiplexing (WDM) optical components. While many researchers have studied on the issue of scheduling messages in both time and wavelength domains in such a network (e.g., [3],[4]), there have been only a few schemes that support variable-length message transmissions without segmentation and reassembly processes: In [6], we studied scheduling algorithms for unslotted Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) with backoff Media Access Control (MAC) protocol to address the issues of fairness and bandwidth efficiency in multiple-access WDM ring networks. In [10], the authors studied distributed algorithms for scheduling variable-length messages in a single-hop multichannel local lightwave network with a major

Service Level Management represents an important and recent shift in network management, since presents a policy-based management model oriented b y user and application profiles. On the other hand, the DiffServ model of the IETF, intends to offer quality of service on the Internet. This work presents and evaluates a functional architecture a nd a framework for mapping service management policies and constraints into DiffServ mechanisms. Various simulation scenarios described through the use of service policies are introduced and analyzed. It is shown that the use of service level management allows for efficient dynamic traffic engineering of DiffServ backbones. Palavras-chave: Qualidade de Serviço, Políticas de Gerenciamento, Gerenciamento de Serviços

4 simple implementation of doubleended priority queues is presented. The proposed structure, called a min-max heap, can be built in linear time; in contrast to conventional heaps, it allows both FindMin and FindMax to be performed in constant time; Insert, DeleteMin, and DeleteMax operations can be performed in logarithmic time. Min-max heaps can be generalized to support other similar order-statistics operations efficiently (e.g., constant time FindMedian and logarithmic time DeleteMedian); furthermore, the notion of min-max ordering can be extended to other heap-ordered structures, such as leftist trees.

We analyze a discrete-time priority queue with train arrivals. Messages of a variable number of fixed-length packets belonging to two classes arrive to the queue at the rate of one packet per slot. We assume geometrically distributed message lengths. Packets of the first class have transmission priority over the packets of the other class. By using probability generating functions, some performance measures such as the moments of the packet delay are calculated. The impact of the priority scheduling discipline and the correlation in the arrival process is shown by some numerical examples.

Priority scheduling for packets is a hot topic, as interactive (voice,video) services are being integrated in existing data networks. In this paper, we consider a discrete-time queueing system with a non-preemptive (or Head-Of-the-Line) priority scheduling discipline and a general number of priority classes. Packets of variable length arrive in the queueing system. We derive expressions for the probability generating functions of the packet delays. From these functions, some performance measures (such as moments and approximate probabilities) are calculated. We illustrate the performance measures by means of some numerical examples and show how to apply the theoretical results to a queue that handles arriving multimedia traffic.

In this paper, we analyze a discrete-time priority queue with a session-based arrival process. We consider an infinitely large user population, where each user can start and end sessions. Sessions belong to one of two classes and generate a variable number of fixed-length packets which arrive to the queue at the rate of one packet per slot. The lengths of the sessions are generally distributed. Packets of the first class have transmission priority over packets of the other class. The model is motivated by E-commerce web servers and web servers handling delay-sensitive and delay-insensitive content. By using probability generating functions, performance measures of the queue such as the moments of the packet delays of both classes are calculated. The impact of the priority scheduling discipline and of the session nature of the arrival process is demonstrated. We furthermore use our analysis to provide specific results for an E-commerce web server.

We consider a discrete-time gated vacation system. The available buffer space is divided into two subsequent queues separated by a gate and new customers arrive either before or after this gate. Whenever all customers after the gate are served, the server takes a vacation. After each vacation, the gate opens which causes all waiting customers to move to the buffer space after the gate. The model under investigation allows to capture performance of a.o. the exhaustive and the gated queueing systems with multiple or single vacations. Using a probability generating functions approach, we obtain expressions for performance measures such as moments of system contents at various epochs in equilibrium and of customer delay. We conclude with a numerical example.

The support for mission critical machine-type-communication (cMTC) services is indispensable for the 5th generation (5G) mobile communication systems. As the cMTC and (part of) the conventional humantype-communication (HTC) services are broadband and delay-sensitive services, how to ensure their coexistence is a new and challenging problem. This paper investigates the problem of service-level resource allocation, which decides how cMTC and HTC traffic share a limited amount of radio resource. Considering a largescale network, we put forth a system model that integrates queuing models and stochastic geometric models to characterize the delay performance in self-interfering scenarios. A service-level resource allocation scheme called load division is proposed. The delay and throughput performance of cMTC and HTC are derived under different resource allocation schemes and priority scheduling policies. We show that compared with the baseline scheme of frequency division, the proposed load division scheme can significantly improve the delay performance of cMTC service, at a cost of slightly degraded MTC and HTC service capacities.