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1.
An M/G/1 retrial queueing system with additional phase of service and possible preemptive resume service discipline is considered. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the server. The steady-state distributions of the server state and the number of customers in the orbit are obtained along with other performance measures. The effects of various parameters on the system performance are analysed numerically. A general decomposition law for this retrial queueing system is established. 相似文献
2.
3.
We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs. 相似文献
4.
Kurt Majewski 《Queueing Systems》2005,50(2-3):199-230
We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20 相似文献
5.
In this article we prove the existence of the solution to the mixed problem for Euler–Bernoulli beam equation with memory term. The existence is proved by means of the Faedo–Galerkin method and the exponential decay is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
6.
We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of
models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the
expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline
at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies
at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different
service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system
reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity
of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering
in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance
with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time
approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is
excellent for practical heavy-traffic scenarios.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律. 相似文献
8.
Xiangtong Qi 《Discrete Applied Mathematics》2007,155(3):416-422
We study a machine scheduling model in which job scheduling and machine maintenance activities have to be considered simultaneously. We develop the worst-case bounds for some heuristic algorithms, including a sharper worst-case bound of the SPT schedule than the results in the literature, and another bound of the EDD schedule. 相似文献
9.
Richard O. LaMaire 《Queueing Systems》1992,11(4):357-375
We define and analyze anM/G/1/N vacation model that uses a service discipline that we call theE-limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied (i.e. exhausted) or a randomly chosen limit ofl customers has been served. The server then goes on a vacation before returning to service the queue again. The queue length distribution and the Laplace-Stieltjes transforms of the waiting time, busy period and cycle time distributions are found. Further, an expression for the mean waiting time is developed. Several previously analyzed service disciplines, including Bernoulli scheduling, nonexhaustive service and limited service, are special cases of the general varying limit discipline that is analyzed in this paper. 相似文献
10.
Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint
distribution of several variables associated with the busy cycle inM/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dualGI/M/1. In this note, we generalize this duality relation toGI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem
is superfluous for the duality relation. 相似文献