Finite Capacity Queueing System Research Articles

A server backup model with Markovian arrivals and phase type services

We consider a finite capacity queueing system with one main server who is supported by a backup server. We assume Markovian arrivals, phase type services, and a threshold-type server backup policy with two pre-determined lower and upper thresholds. A request for a backup server is made whenever the buffer size (number of customers in the queue) hits the upper threshold and the backup server is released from the system when the buffer size drops to the lower threshold or fewer at a service completion of the backup server. The request time for the backup server is assumed to be exponentially distributed. For this queuing model we perform the steady state analysis and derive a number of performance measures. We show that the busy periods of the main and backup servers, the waiting times in the queue and in the system, are of phase type. We develop a cost model to obtain the optimal threshold values and study the impact of fixed and variable costs for the backup server on the optimal server backup decisions. We show that the impact of standard deviations of the interarrival and service time distributions on the server backup decisions is quite different for small and large values of the arrival rates. In addition, the pattern of use of the backup server is very different when the arrivals are positively correlated compared to mutually independent arrivals.

STOCHASTIC MODELING AND ANALYSIS OF AN ACTIVE CONGESTION CONTROL PROTOCOL UNDER DIFFERENTIATED BURSTY TRAFFIC

Traffic congestion degrades not only the user-perceived Quality-of-Service (QoS), such as leading to high packet loss rates, low throughput, and increased delays, but also causes excessive energy consumption in energy-sensitive systems (e.g., wireless sensor networks). A simple way to detect congestion is to monitor and measure queue length in network nodes or routers. This paper develops an analytical performance model for a finite capacity queueing system with an enhanced Random Early Detection (RED) congestion control scheme based on the instantaneous queue length in the presence of differentiated classes of bursty traffic. The aggregate traffic is captured by the superposition of 2-state Markov Modulated Poisson Processes (MMPP). The individual threshold is assigned to each traffic class in order to differentially control traffic injection rate. The accuracy of this model is verified by comparing the analytical results against those obtained from simulation experiments. The model is adopted to investigate the effects of traffic burstiness and system capacity on the performance of the congestion control scheme.

Modeling and evaluation of congestion control for different classes of network traffic

AbstractTraffic congestion has become a crucial problem in wireless networks due to its detrimental effects on the end‐to‐end Quality‐of‐Service (QoS) of mobile users. This issue has posed various challenges to developing effective congestion control mechanisms and devising new performance evaluation tools. Various congestion control schemes have been proposed to support differentiated QoS. Among these schemes, Active Queue Management (AQM) has been recognized as an effective mechanism to manage downlink buffers in wireless networks. Most existing studies on AQM are based on the use of averaged queue length and the related performance analysis is carried out via software simulation. This paper contributes to the development of an analytical performance model for a finite capacity queuing system subject to AQM and multiple traffic classes based on the instantaneous queue length. Expressions for the aggregated and marginal performance metrics including the mean queuing length, packet loss probability, mean waiting time, system throughput, response time, and utilization are analytically derived. The validity of this new model is demonstrated by comparing the analytical results against those obtained from simulation experiments. The analytical model is then used to investigate the effects of varying thresholds on the aggregated and marginal performance metrics under different combinations of arriving rates for multiple traffic classes. Copyright © 2007 John Wiley & Sons, Ltd.

Optimal prices for finite capacity queueing systems

We prove a lower bound on the optimal price for a fairly large class of blocking systems with general arrival and service processes, determine optimal price expressions for M/M/1/m and M/GI/s/s systems, and investigate how optimal prices change with changes in the size of the waiting room and service capacity.

A single-server finite-capacity queueing system with Markov flow and discrete-time service

Concepts of a discrete Markov flow and discrete-time Markov service are defined. A single-server finite-capacity queueing system with Markov flow and discrete-time service is studied. An algorithm for computing the stationary state probability distribution of the system is designed. The main performance characteristics, such as the stationary loss probability and mean waiting time for service, are determined.

Parametric nonlinear programming for analyzing fuzzy queues with finite capacity

This paper proposes a procedure for constructing the membership functions of the performance measures in finite-capacity queueing systems with the arrival rate and service rate being fuzzy numbers. The basic idea is to transform a fuzzy queue with finite capacity to a family of conventional crisp queues with finite capacity by applying the α-cut approach. A pair of parametric nonlinear programs is formulated to describe the family of crisp finite-capacity queues, via which the membership functions of the performance measures are derived. To demonstrate the validity of the proposed procedure, two fuzzy queues often encountered in real life serve as examples. Since the performance measures are expressed by membership functions rather than by crisp values, more information is provided for designing queueing systems in real life. By extending to fuzzy environment, the finite-capacity queueing models would have wider applications.

Perturbation Analysis of Multiclass Stochastic Fluid Models

We use a stochastic fluid model (SFM) to capture the operation of finite-capacity queueing systems with multiple customer classes. We derive gradient estimators for class-dependent loss and workload related performance metrics with respect to any one of several threshold parameters used for buffer control. These estimators are shown to be unbiased and directly observable from a sample path without any knowledge of underlying stochastic characteristics of the traffic processes. This renders them computable in on-line environments and easily implementable in settings such as communication networks.

Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/Hk/1 Queueing System

We consider a single removable and non-reliable server in both infinite capacity and finite capacity queueing systems with Poisson arrivals and ¿-type hyper-exponential distribution for the service times operating under the N policy. The server may be turned on at arrival epochs or off at departure epochs. Breakdown and repair times of the server are assumed to follow a negative exponential distribution. Cost model for infinite capacity queueing system (say cost model 1) is developed to determine the optimal operating policy. Cost model for finite capacity queueing system (say cost model 2) is developed to determine the optimal operating policy and the optimal system capacity, simultaneously. This paper presents the optimal operating policy, the optimal system capacity, the minimum expected cost based on specific values given to the system parameters, as well as to the cost elements. The sensitivity analysis is also investigated.

Bias optimal admission control policies for a multiclass nonstationary queueing system

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

Bias optimal admission control policies for a multiclass nonstationary queueing system

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

On finite capacity queueing systems with a general vacation policy

We consider a Poisson arrival queueing system with finite capacity and a general vacation policy as described in Loris‐Teghem [Queueing Systems 3 (1988), 41‐52]. From our previous results regarding the stationary queue length distributions immediately after a departure and at an arbitrary epoch, we derive a relation between both distributions which extends a result given in Frey and Takahashi [Operations Research Letters 21 (1997), 95‐100] for the particular case of an exhaustive service multiple vacation policy.

BIAS OPTIMALITY IN A QUEUE WITH ADMISSION CONTROL

We consider a finite capacity queueing system in which each arriving customer offers a reward. A gatekeeper decides based on the reward offered and the space remaining whether each arriving customer should be accepted or rejected. The gatekeeper only receives the offered reward if the customer is accepted. A traditional objective function is to maximize the gain, that is, the long-run average reward. It is quite possible, however, to have several different gain optimal policies that behave quite differently. Bias and Blackwell optimality are more refined objective functions that can distinguish among multiple stationary, deterministic gain optimal policies. This paper focuses on describing the structure of stationary, deterministic, optimal policies and extending this optimality to distinguish between multiple gain optimal policies. We show that these policies are of trunk reservation form and must occur consecutively. We then prove that we can distinguish among these gain optimal policies using the bias or transient reward and extend to Blackwell optimality.

A maximum entropy optimization approach to tandem queues with generalized blocking

We study a general blocking scheme for an open tandem queueing network with finite intermediate buffers. The service time at each node as well as interarrival time at the first node is assumed to be exponentially distributed. The interarrival and service time at each intermediate node of the tandem queue, under the general blocking scheme, depend upon three parameters at each node, namely, the maximum number of raw jobs, the upper limit on the number of finished but blocked jobs and the buffer capacity. This three-parameter analysis was introduced by Cheng and Yao (1993), and was shown, using Monte Carlo simulations, to provide good results. Our analysis is also based on this three-parameter approach, but with a different view. We first decompose the tandem queue into a group of two-node subsystems in order to derive a set of equations for the effective interarrival and service time distributions at each node. Each of these two-node subsystems is treated as a finite capacity queueing system with population size constraints. Then we apply the principle of maximum entropy to evaluate different parameters such as the blocking probabilities, starvation probabilities, etc., of each subsystem. We propose a step-by-step algorithm along with its convergence properties. A comparison of numerical results with the simulation results is also discussed.

Loss periods in ATM output multiplexer

The authors present a new approach to evaluating the loss periods in the output multiplexer of ATM switch. First, they present a model for the output multiplexer using a discrete time finite capacity queueing system model with a threshold in the queue and priority in the bursty incoming cells. In modelling the loss period, they divide the queue space into a nonloss region, a half-loss region and a full-loss region, and define their corresponding time periods as the nonloss period, half-loss period and full-loss period, respectively. Next, they derive a general formula for the mean sojourn time for which a queue stays in a region. They derive formulae for the loss period, cell loss rate due to buffer overflow, discard rate for low priority cell and cell waiting time. Finally, they present the results of numerical experiments.

A finite capacity queue with Markovian arrivals and two servers with group services

In this paper we consider a finite capacity queuing system in which arrivals are governed by a Markovian arrival process. The system is attended by two exponential servers, who offer services in groups of varying sizes. The service rates may depend on the number of customers in service. Using Markov theory, we study this finite capacity queuing model in detail by obtaining numerically stable expressions for (a) the steady‐state queue length densities at arrivals and at arbitrary time points; (b) the Laplace‐Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. The stationary waiting time distribution is shown to be of phase type when the interarrival times are of phase type. Efficient algorithmic procedures for computing the steady‐state queue length densities and other system performance measures are discussed. A conjecture on the nature of the mean waiting time is proposed. Some illustrative numerical examples are presented.

Optimal routing and buffer allocation for a class of finite capacity queueing systems

The problem of routing jobs to K parallel queues with identical exponential servers and unequal finite buffer capacities is considered. Routing decisions are taken by a controller which has buffering space available to it and may delay routing of a customer to a queue. Using ideas from weak majorization, it is shown that the shorter nonfull queue delayed (SNQD) policy minimizes both the total number of customers in the system at any time and the number of customers that are rejected by that time. The SNQD policy always delays routing decisions as long as all servers are busy. Only when all the buffers at the controller are occupied is a customer routed to the queue with the shortest queue length that is not at capacity. Moreover, it is shown that, if a fixed number of buffers is to be distributed among the K queues, then the optimal allocation scheme is the one in which the difference between the maximum and minimum queue capacities is minimized, i.e. becomes either 0 or 1.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computational analysis of a finite capacity queueing system with vacations and nonexhaustive service

We give an elementary treatment of the M/G/l/N queue with vacations and a break following on every service. Using the method of phases and the regenerative properties of the queueing process we derive an algorithmic solution for the stationary distributions of both the queue length and the waiting times for accepted customers.

A solvable model for a finite-capacity queueing system

A solvable model for a finite-capacity queueing system

A solvable model for a finite-capacity queueing system

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A solvable model for a finite-capacity queueing system

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.