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本文研究批量到达带启动时间的单重休假的M/G/1排队系统,给出稳态队长的母函数和等待时间分布的LST及其它们的随机分解结果,推导出忙期、闲期和线期母函数和均值。 相似文献
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本文介绍了带有各种休假策略的M/M/C休假排队的研究方法及结果,在所有服务台全的条件下,我们证明了系统的稳态队长和稳态等待时间可分解成两个独立随机变量和和,其中一个随机变量愉是相应的经典M/M/C排队的稳态队长与稳态等待时间。 相似文献
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同步休假GI/M/c排队的稳态理论 总被引:10,自引:1,他引:9
本文研究同步多重休假的GI/M/c排队系统,休假时间服从指数分布,使用发展了矩阵几何解决方法,给出了系统的平衡条件、稳态队长及等等时间分布。证明了队长和等等时间的条件随机分解定理,并讨论了由休假引起的附加队长和附加延迟的位相(PH)结构。 相似文献
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Mor Harchol-Balter Takayuki Osogami Alan Scheller-Wolf Adam Wierman 《Queueing Systems》2005,51(3-4):331-360
We present the first near-exact analysis of an M/PH/k queue with m > 2 preemptive-resume priority classes. Our analysis introduces a new technique, which we refer to as Recursive Dimensionality
Reduction (RDR). The key idea in RDR is that the m-dimensionally infinite Markov chain, representing the m class state space, is recursively reduced to a 1-dimensionally infinite Markov chain, that is easily and quickly solved.
RDR involves no truncation and results in only small inaccuracy when compared with simulation, for a wide range of loads and
variability in the job size distribution.
Our analytic methods are then used to derive insights on how multi-server systems with prioritization compare with their single
server counterparts with respect to response time. Multi-server systems are also compared with single server systems with
respect to the effect of different prioritization schemes—“smart” prioritization (giving priority to the smaller jobs) versus
“stupid” prioritization (giving priority to the larger jobs). We also study the effect of approximating m class performance by collapsing the m classes into just two classes.
Supported by NSF Career Grant CCR-0133077, NSF Theory CCR-0311383, NSF ITR CCR-0313148, and IBM Corporation via Pittsburgh
Digital Greenhouse Grant 2003.
AMS subject classification: 60K25, 68M20, 90B22, 90B36 相似文献
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带有负顾客的N策略工作休假M/M/1排队 总被引:1,自引:0,他引:1
考虑带有正、负顾客的N策略工作休假M/M/1排队。负顾客一对一抵消队尾的正顾客(若有),若系统中无正顾客,到达的负顾客自动消失,负顾客不接受服务。在休假期间,服务员并未完全停止工作而是以较低的服务率为顾客服务。用拟生灭过程和矩阵几何解方法,我们给出了稳态队长和稳态等待时间的分布。此外,我们也证明了稳态条件下的队长和等待时间的条件随机分解并得到了附加队长和附加延迟的分布。 相似文献
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Zhe George Zhang 《Queueing Systems》2005,51(1-2):173-186
In this paper, we study an M/M/c queue with a three threshold vacation policy denoted by (e, d, N). With such a policy, the servers keep serving the customers until the number of idle servers reaches d and then e of d servers start taking a vacation together. These e servers keep taking vacations until the number of customers in the system is at least N at a vacation completion instant, then the e servers return to serve the queue again. Using the matrix analytic method, we obtain the stationary performance measures
and prove the conditional stochastic decomposition properties for the waiting time and queue length. This model is a generalization
of previous multi-server vacation models and offers a useful performance evaluation and system design tool in multi-task server
queueing systems. 相似文献
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Wojciech M. Kempa 《随机分析与应用》2013,31(1):26-43
A batch arrival queueing system with a single vacation between two successive busy periods and with exhaustive service is considered. The departure process h(t) is studied first on a single vacation cycle. The approach based on renewal theory is applied to obtain results in the general case. In particular, the explicit representation for the generating function of Laplace transform of the probability function of h(t) is derived. All formulae are written in terms of input parameters of the system and factors of a certain canonical factorization of Wiener–Hopf type. A numerical approach to results is discussed as well. 相似文献
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该文研究在D-策略控制下服务员单重休假且休假不中断的M/G/1 排队系统,其中当服务员休假结束归来时,如果系统中等待服务的顾客所需的总服务时间之和不小于事先给定的正数阀值D,服务员就立即开始服务.运用全概率分解技术、更新过程理论和拉普拉斯变换工具,本文在任意初始状态下讨论了队长的瞬态分布,导出了队长瞬态分布的拉普拉斯变... 相似文献
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We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies. 相似文献
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We show in this paper that the computation of the distribution of the sojourn time of an arbitrary customer in a M/M/1 with the processor sharing discipline (abbreviated to M/M/1 PS queue) can be formulated as a spectral problem for a self-adjoint operator. This approach allows us to improve the existing results for this queue in two directions. First, the orthogonal structure underlying the M/M/1 PS queue is revealed. Second, an integral representation of the distribution of the sojourn time of a customer entering the system while there are n customers in service is obtained. 相似文献
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We study a discrete-time GI/Geo/1 queue with server vacations. In this queueing system, the server takes vacations when the system does not have any waiting customers at a service completion instant or a vacation completion instant. This type of discrete-time queueing model has potential applications in computer or telecommunication network systems. Using matrix-geometric method, we obtain the explicit expressions for the stationary distributions of queue length and waiting time and demonstrate the conditional stochastic decomposition property of the queue length and waiting time in this system. 相似文献
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We obtain the exact convergence rate of the stationary distribution (K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution of the embedded Markov chain in GI/M/c queue as K. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c=1 by nontrivial ways. Our results also strengthen the Simonot's results [5]. 相似文献
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Many models for customers impatience in queueing systems have been studied in the past; the source of impatience has always
been taken to be either a long wait already experienced at a queue, or a long wait anticipated by a customer upon arrival.
In this paper we consider systems with servers vacations where customers’ impatience is due to an absentee of servers upon arrival. Such a model, representing frequent behavior by waiting customers in service systems, has never
been treated before in the literature. We present a comprehensive analysis of the single-server, M/M/1 and
M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form results. In particular, we show
that the proportion of customer abandonments under the single-vacation regime is smaller than that under the multiple-vacation
discipline.
This work was supported by the Euro-Ngi network of excellence. 相似文献
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Negative arrivals are used as a control mechanism in many telecommunication and computer networks. In the paper we analyze multiserver retrial queues; i.e., any customer finding all servers busy upon arrival must leave the service area and re-apply for service after some random time. The control mechanism is such that, whenever the service facility is full occupied, an exponential timer is activated. If the timer expires and the service facility remains full, then a random batch of customers, which are stored at the retrial pool, are automatically removed. This model extends the existing literature, which only deals with a single server case and individual removals. Two different approaches are considered. For the stable case, the matrix–analytic formalism is used to study the joint distribution of the service facility and the retrial pool. The approximation by more simple infinite retrial model is also proved. In the overloading case we study the transient behaviour of the trajectory of the suitably normalized retrial queue and the long-run behaviour of the number of busy servers. The method of investigation in this case is based on the averaging principle for switching processes. 相似文献
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This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form
U ∧ K for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than
. We study the compound Poisson ruin probability ψ(u) or, equivalently, the tail
of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of ψ(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times,
and compare the results to different approximations of ψ(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we
investigate the asymptotics as K → ∞ of the asymptotic exponential decay rate γ = γ
(K) in a more general truncated Lévy process setting, and give a discussion of some of the implications for the approximations.
AMS 2000 Subject Classification Primary 68M20, Secondary 60K25
†Partially supported by MaPhySto—A Network in Mathematical Physics and Stochastics, founded by the Danish National Research
Foundation.
An erratum to this article is available at . 相似文献