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151.
In this note, we consider the steady-state probability of delay (PW) in the C2/G/1 queue and the steady-state probability of loss (ploss) in the C2/G/1 loss system, in both of which the interarrival time has a two-phase Coxian distribution. We show that, for cX
2<1, where cX is the coefficient of variation of the interarrival time, both ploss and PW are increasing in β(s), the Laplace–Stieltjes transform of the general service-time distribution. This generalises
earlier results for the GE2/G/1 queue and the GE2/G/1 loss system. The practical significance of this is that, for cX
2<1, ploss in the C2/G/1 loss system and PW in the C2/G/1 queue are both increasing in the variability of the service time.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
152.
We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index -ν, ν non-integer,
iff the sojourn time distribution is regularly varying of index -ν. This result is derived from a new expression for the Laplace–Stieltjes
transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution.
We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojourn time
distribution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic
limiting sojourn time distribution when the service time distribution is regularly varying. Explicit formulas and multiterm
expansions are provided for the case that the service time has a Pareto distribution.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
153.
A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity 总被引:5,自引:0,他引:5
We study a single removable server in an infinite and a finite queueing systems with Poisson arrivals and general distribution service times. The server may be turned on at arrival epochs or off at service completion epochs. We present a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to obtain the steady state probability distribution of the number of customers in a finite system. The method is illustrated analytically for three different service time distributions: exponential, 3-stage Erlang, and deterministic. Cost models for infinite and finite queueing systems are respectively developed to determine the optimal operating policy at minimum cost. 相似文献
154.
155.
The M/G/1 queue with impatient customers is studied. The complete formula of the limiting distribution of the virtual waiting time is derived explicitly. The expected busy period of the queue is also obtained by using a martingale argument. 相似文献
156.
157.
We study a PH/G/1 queue in which the arrival process and the service times depend on the state of an underlying Markov chain J(t) on a countable state spaceE. We derive the busy period process, waiting time and idle time of this queueing system. We also study the Markov modulated EK/G/1 queueing system as a special case. 相似文献
158.
We consider an M/PH/1 queue with balking based on the workload. An arriving customer joins the queue and stays until served only if the system
workload is below a fixed level at the time of arrival. The steady state workload distribution in such a system satisfies
an integral equation. We derive a differential equation for Phase type service time distribution and we solve it explicitly,
with Erlang, Hyper-exponential and Exponential distributions as special cases. We illustrate the results with numerical examples. 相似文献
159.
We consider a system ofN queues served by a single server in cyclic order. Each queue has its own distinct Poisson arrival stream and its own distinct general service-time distribution (asymmetric queues), and each queue has its own distinct distribution of switchover time (the time required for the server to travel from that queue to the next). We consider two versions of this classical polling model: In the first, which we refer to as the zero-switchover-times model, it is assumed that all switchover times are zero and the server stops traveling whenever the system becomes empty. In the second, which we refer to as the nonzero-switchover-times model, it is assumed that the sum of all switchover times in a cycle is nonzero and the server does not stop traveling when the system is empty. After providing a new analysis for the zero-switchover-times model, we obtain, for a host of service disciplines, transform results that completely characterize the relationship between the waiting times in these two, operationally-different, polling models. These results can be used to derive simple relations that express (all) waiting-time moments in the nonzero-switchover-times model in terms of those in the zero-switchover-times model. Our results, therefore, generalize corresponding results for the expected waiting times obtained recently by Fuhrmann [Queueing Systems 11 (1992) 109—120] and Cooper, Niu, and Srinivasan [to appear in Oper. Res.].Research supported in part by the National Science Foundation under grant DDM-9001751. 相似文献
160.