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1.
2.
W. Stadje 《Queueing Systems》1989,4(1):85-92
For a M/M/1 queueing system with group arrivals of random size the transition probabilities of the queue size process and the distribution of the maximal queue size during a time interval [0,t) are calculated. Simple formulae for the corresponding Laplace transforms are given. 相似文献
3.
Peixia Gao Sabine Wittevrongel Joris Walraevens Herwig Bruneel 《Mathematical Methods of Operations Research》2008,67(2):269-284
In this paper, we study the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive
at the system according to a two-state Markovian arrival process. The service times of the packets are assumed to be constant,
equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on probability generating
functions (PGF’s). Explicit expressions are obtained for the PGF’s of the system contents and the packet delay. From these,
the mean values, the variances and the tail distributions of the system contents and the packet delay are calculated. Numerical
examples are given to show the influence of various model parameters on the system behavior. 相似文献
4.
We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GI
X
/M//n systems with state dependent services rates, also denoted as GI
X
/M(m)−M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in
the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear
system of equations. The results derived are illustrated for specific sets of parameters. 相似文献
5.
Dieter Fiems Stijn De Vuyst Sabine Wittevrongel Herwig Bruneel 《Annals of Operations Research》2009,170(1):113-131
In this contribution we investigate higher-order loss characteristics for M/G/1/N queueing systems. We focus on the lengths of the loss and non-loss periods as well as on the number of arrivals during these
periods. For the analysis, we extend the Markovian state of the queueing system with the time and number of admitted arrivals
since the instant where the last loss occurred. By combining transform and matrix techniques, expressions for the various
moments of these loss characteristics are found. The approach also yields expressions for the loss probability and the conditional
loss probability. Some numerical examples then illustrate our results. 相似文献
6.
A product form equilibrium distribution is derived for a class of queueing networks in either discrete or continuous time,
in which multiple customers arrive simultaneously and batches of customers complete service simultaneously. 相似文献
7.
We derive fast recursions to compute the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability, for regular and oscillating M
X
/G/1/n systems. 相似文献
8.
We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献
9.
We study the vessel arrival process in bulk ports handling either cargo containers or minerals. Then we introduce the SHIP/G/1 queue to be able to study the queueing behavior at the port. We present approximations for the asymptotic probabilities of delay and the number of vessels at the port. Numerical examples show the accuracy of the approximations. In appendices, we provide details of the analysis of the number of vessels at the port and the correlation properties of the vessel arrival process. 相似文献
10.
本文首次研究服务员具有多重休假规则的成批到达Mx/G/1排队系统的输出过程.应用更新过程理论、拉普拉斯-司梯阶变换和本文提出的直接概率分解分析法,讨论了从任意初始状态出发,系统在(0,t]时间内输出顾客的平均数,以及其渐近展开,得到一些重要结果. 相似文献