2,278 research outputs found

    The MVA Priority Approximation

    Get PDF
    A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation

    A Fixed-Point Algorithm for Closed Queueing Networks

    Get PDF
    In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)

    Validity of heavy traffic steady-state approximations in generalized Jackson Networks

    Full text link
    We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavy-traffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian motion (RBM) in the orthant, as the traffic intensity approaches unity. However, barring simple instances, it is still not known whether the stationary distribution of RBM provides a valid approximation for the steady-state of the original network. In this paper we resolve this open problem by proving that the re-scaled stationary distribution of the GJN converges to the stationary distribution of the RBM, thus validating a so-called ``interchange-of-limits'' for this class of networks. Our method of proof involves a combination of Lyapunov function techniques, strong approximations and tail probability bounds that yield tightness of the sequence of stationary distributions of the GJN.Comment: Published at http://dx.doi.org/10.1214/105051605000000638 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    On closed queueing networks with mixed preemptive resume priority servers.

    Get PDF
    This paper discusses a typical closed queueing network model in which multiple preemptive resume servers are present with different priority structures at each priority node. An algorithm is developed that is applicable for the three-node two-class model and results are compared to point estimates obtained from simulation. The algorithm is partly based on the Delay/MVA algorithm developed by Bondi and Chuang, because of the accuracy with which instant arrival queue lengths at fcfs servers are calculated. Results are also compared with results obtained from the Shadow Approximation.Networks;

    Monotonicity and error bounds for networks of Erlang loss queues

    Get PDF
    Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably\ud (i) classical circuit switch telephone networks (loss networks) and\ud (ii) present-day wireless mobile networks.\ud \ud Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it has not in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hyper cubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to\ud \ud - secure upper bounds for loss probabilities and\ud - analytic error bounds for the accuracy of the approximation for various performance measures.\ud \ud The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:\ud \ud - pure loss networks as under (i)\ud - GSM-networks with fixed channel allocation as under (ii).\ud \ud The results are of practical interest for computational simplifications and, particularly, to guarantee blocking probabilities not to exceed a given threshold such as for network dimensioning.\u

    Integrated performance evaluation of extended queueing network models with line

    Get PDF
    Despite the large literature on queueing theory and its applications, tool support to analyze these models ismostly focused on discrete-event simulation and mean-value analysis (MVA). This circumstance diminishesthe applicability of other types of advanced queueing analysis methods to practical engineering problems,for example analytical methods to extract probability measures useful in learning and inference. In this toolpaper, we present LINE 2.0, an integrated software package to specify and analyze extended queueingnetwork models. This new version of the tool is underpinned by an object-oriented language to declarea fairly broad class of extended queueing networks. These abstractions have been used to integrate in acoherent setting over 40 different simulation-based and analytical solution methods, facilitating their use inapplications

    Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems

    Get PDF
    Includes bibliographical references (p. 41-45).Research supported by Fundac̦ão de Amparo a Pesquisa do Estado de São Paulo, Brazil.by Gabriel R. Bitran, Reinaldo Morabito
    corecore