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1.
We propose a simple way, called the arrival time approach, of finding the queue length distributions for M/G/1-type queues with generalized server vacations. The proposed approach serves as a useful alternative to understanding complicated queueing processes such as priority queues with server vacations and MAP/G/1 queues with server vacations. 相似文献
2.
V. Anantharam 《Queueing Systems》1987,2(4):387-392
Given a finite number of empty ./M/1 queues, let customers arrive according to an arbitrary arrival process and be served at each queue exactly once, in some fixed order. The process of departing customers from the network has the same law, whatever the order in which the queues are visited. This remarkable result, due to R. Weber [4], is given a simple probabilistic proof. 相似文献
3.
M/M/1算子的特征值及其应用(英文) 总被引:1,自引:1,他引:0
讨论 M/M/1算子的谱特征,证明0是 M/M/1算子的几何重数为 1的特征值,并且对应的特征向量是正的,作为应用给出了排队论中四个指标:系统中顾客的平均逗留时间,顾客的平均等待时间,顾客总数及等待的顾客总数的计算方法. 相似文献
4.
We consider theM/M/c queue, where customers transfer to a critical state when their queueing (sojourn) time exceeds a random time. Lower and upper bounds for the distribution of the number of critical jobs are derived from two modifications of the original system. The two modified systems can be efficiently solved. Numerical calculations indicate the power of the approach. 相似文献
5.
Arzad A. Kherani 《Queueing Systems》2006,53(3):159-169
In this paper we present a direct approach to obtaining joint distributions of various quantities of interest in a busy period
in an M/M/1 queue. These quantities are: the sojourn times and waiting times of all the customers in the busy period, the busy period length and the number of customers served in a busy period. Since the evolution
of the total workload process between two successive customer arrivals is deterministic, this work gives statistic of the
complete evolution of the workload process within a busy period.
This work was done when the author was post doctoral fellow with the MAESTRO group at INRIA, Sophia Antipolis, France, and
was supported by project no. 2900-IT-1 from the Centre Franco-Indien pour la Promotion de la Recherche Avancee (CEFIPRA). 相似文献
6.
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
7.
The paper deals with the workload and busy period for the $M/GI/1$ M / G I / 1 system with impatience under FCFS discipline. The customers may become impatient during their waiting for service with generally distributed maximal waiting times and also during their service with generally distributed maximal service times depending on the time waited for service. This general impatience mechanism was originally introduced by Kovalenko (1961) and considered by Daley (1965), too. It covers the special cases of impatience on waiting times as well as impatience on sojourn times, for which Boxma et al. (2010, 2011) gave new results and outlined special cases recently. Our unified approach bases on the vector process of workload and busy time. Explicit representations for the LSTs of workload and busy period are given in case of phase-type distributed impatience. 相似文献
8.
Uri Yechiali 《Queueing Systems》2007,56(3-4):195-202
Consider a system operating as an M/M/c queue, where c=1, 1<c<∞, or c=∞. The system as a whole suffers occasionally a disastrous breakdown, upon which all present customers (waiting and served)
are cleared from the system and lost. A repair process then starts immediately. When the system is down, inoperative, and
undergoing a repair process, new arrivals become impatient: each individual customer, upon arrival, activates a random-duration
timer. If the timer expires before the system is repaired, the customer abandons the queue never to return. We analyze this
model and derive various quality of service measures: mean sojourn time of a served customer; proportion of customers served; rate of lost customers due to disasters; and rate of abandonments due to impatience.
相似文献
9.
This paper considers theM/M/c queue in which a customer leaves when its service has not begun within a fixed interval after its arrival. The loss probability
can be expressed in a simple formula involving the waiting time probabilities in the standardM/M/c queue. The purpose of this paper is to give a probabilistic derivation of this formula and to outline a possible use of this
general formula in theM/M/c retrial queue with impatient customers.
This research was supported by the INTAS 96-0828 research project and was presented at the First International Workshop on
Retrial Queues, Universidad Complutense de Madrid, Madrid, September 22–24, 1998. 相似文献
10.
We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period. It enables as a by-product to prove that the process of instants of beginning of services is not Poisson. We then proceed to a more precise analysis. We consider a family of polynomial generating series associated with Dyck paths of length 2n and we show that they provide the correlation function of the successive services in a busy period with n+1 customers. 相似文献
11.
12.
S.W Fuhrmann 《Operations Research Letters》1985,4(3):139-144
Consider a symmetrical system of n queues served in cyclic order by a single server. It is shown that the stationary number of customers in the system is distributed as the sum of three independent random variables, one being the stationary number of customers in a standard M/G/1 queue. This fact is used to establish an upper bound for the mean waiting time for the case where at most k customers are served at each queue per visit by the server. This approach is also used to rederive the mean waiting times for the cases of exhaustive service, gated service, and serve at most one customer at each queue per visit by the server. 相似文献
13.
René Bekker 《Queueing Systems》2005,50(2-3):231-253
We consider M/G/1 queues with workload-dependent arrival rate, service speed, and restricted accessibility. The admittance of customers typically depends on the amount of work found upon arrival in addition to its own service requirement. Typical examples are the finite dam, systems with customer impatience and queues regulated by the complete rejection discipline. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet.First, we compare the steady-state distribution of the workload in two finite-buffer models, in which the ratio of arrival and service speed is equal. Second, we find an explicit expression for the cycle maximum in an M/G/1 queue with workload-dependent arrival and service rate. And third, we derive a formal solution for the steady-state workload density in case of restricted accessibility. The proportionality relation between some finite and infinite-buffer queues is extended. Level crossings and Volterra integral equations play a key role in our approach.AMS subject classification: 60K25, 90B22 相似文献
14.
David L. Jagerman Benjamin Melamed 《Methodology and Computing in Applied Probability》2003,5(2):159-181
A call center is a facility for delivering telephone service, both incoming and outgoing. This paper addresses optimal staffing of call centers, modeled as M/G/n queues whose offered traffic consists of multiple customer streams, each with an individual priority, arrival rate, service distribution and grade of service (GoS) stated in terms of equilibrium tail waiting time probabilities or mean waiting times. The paper proposes a methodology for deriving the approximate minimal number of servers that suffices to guarantee the prescribed GoS of all customer streams. The methodology is based on an analytic approximation, called the Scaling-Erlang (SE) approximation, which maps the M/G/n queue to an approximating, suitably scaled M/G/1 queue, for which waiting time statistics are available via the Pollaczek-Khintchine formula in terms of Laplace transforms. The SE approximation is then generalized to M/G/n queues with multiple types of customers and non-preemptive priorities, yielding the Priority Scaling-Erlang (PSE) approximation. A simple goal-seeking search, utilizing SE/PSE approximations, is presented for the optimal staffing level, subject to GoS constraints. The efficacy of the methodology is demonstrated by comparing the number of servers estimated via the PSE approximation to their counterparts obtained by simulation. A number of case studies confirm that the SE/PSE approximations yield optimal staffing results in excellent agreement with simulation, but at a fraction of simulation time and space. 相似文献
15.
16.
Hideaki Takagi 《Queueing Systems》1993,14(1-2):79-98
A steady-state analysis is given for M/G/1/K queues with combinedN-policy and setup times before service periods. The queue length distributions and the mean waiting times are obtained for the exhaustive service system, the gated service system, the E-limited service system, and the G-limited service system. Numerical examples are also provided. 相似文献
17.
This paper gives a transient analysis of the classic M/M/1 and M/M/1/K queues. Our results are asymptotic as time and queue length become simultaneously large for the infinite capacity queue, and as the system’s storage capacity K becomes large for the finite capacity queue. We give asymptotic expansions for pn(t), which is the probability that the system contains n customers at time t. We treat several cases of initial conditions and different traffic intensities. The results are based on (i) asymptotic expansion of an exact integral representation for pn(t) and (ii) applying the ray method to a scaled form of the forward Kolmogorov equation which describes the time evolution of pn(t). 相似文献
18.
Roy D. Yates 《Queueing Systems》1994,18(1-2):107-116
A class of discrete-timeM/G/1 queues, including both round robin and last come first served service, in which customers are subject to permutations is considered. These time slotted queues, analogous to the symmetric queues of Kelly, are analyzed by examination of the time reversed process. Product form stationary distributions are found for a type of doubly stochastic server of Schassberger [5] and for a Bernoulli arrival process queue model of Henderson and Taylor [2]. 相似文献
19.
In this article, we consider a single-server, finite-capacity queue with random bulk service rule where customers arrive according to a discrete-time Markovian arrival process (D-MAP). The model is denoted by D-MAP/G Y /1/M where server capacity (bulk size for service) is determined by a random variable Y at the starting point of services. A simple analysis of this model is given using the embedded Markov chain technique and the concept of the mean sojourn time of the phase of underlying Markov chain of D-MAP. A complete solution to the distribution of the number of customers in the D-MAP/G Y /1/M queue, some computational results, and performance measures such as the average number of customers in the queue and the loss probability are presented. 相似文献
20.
In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform. 相似文献