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1.
《随机分析与应用》2013,31(3):739-753
Abstract We consider an M x /G/1 queueing system with a random setup time, where the service of the first unit at the commencement of each busy period is preceded by a random setup time, on completion of which service starts. For this model, the queue size distributions at a random point of time as well as at a departure epoch and some important performance measures are known [see Choudhury, G. An M x /G/1 queueing system with setup period and a vacation period. Queueing Sys. 2000, 36, 23–38]. In this paper, we derive the busy period distribution and the distribution of unfinished work at a random point of time. Further, we obtain the queue size distribution at a departure epoch as a simple alternative approach to Choudhury4. Finally, we present a transform free method to obtain the mean waiting time of this model. 相似文献
2.
This paper examines an M[x]/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 − p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the Jth vacation, the server becomes idle in the system. Whenever one or more customers arrive at server idle state, the server immediately starts providing service for the arrivals. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair time has a general distribution. For such a system, we derive the distributions of important system characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, the distributions of idle period, busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p∗, J∗) at a minimum cost, and some numerical examples are presented for illustrative purpose. 相似文献
3.
This paper studies the operating characteristics of an M[x]/G/1 queueing system with N-policy and at most J vacations. The server takes at most J vacations repeatedly until at least N customers returning from a vacation are waiting in the queue. If no customer arrives by the end of the Jth vacation, the server becomes idle in the system until the number of arrivals in the queue reaches N. We derive the system size distribution at a random epoch and departure epoch, as well as various system characteristics. 相似文献
4.
This paper studies the operating characteristics of an M[x]/G/1 queueing system under a modified vacation policy, where the server leaves for a vacation as soon as the system is empty. The server takes at most J vacations repeatedly until at least one customer is found waiting in the queue when the server returns from a vacation. We derive the system size distribution at different points in time, as well as the waiting time distribution in the queue. Further, we derive some important characteristics including the expected length of the busy period and idle period. This shows that the results generalize those of the multiple vacation policy and the single vacation policy M[x]/G/1 queueing system. Finally, a cost model is developed to determine the optimum of J at a minimum cost. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
5.
具有可变到达率的多重休假Geo~(λ_1,λ_2)/G/1排队分析 总被引:1,自引:0,他引:1
本文考虑顾客到达与服务员休假相关的多重休假离散时间排队系统,用更新过程及u-变换分析了系统的队长性质.分别得到系统在三种时点(n~-,n~+,n)处的队长分布的递推解,进而揭示了在不同到达率条件下系统队长分布不再具有随机分解特性,得到了系统在四种时点(n~-,n~+,n,离去时点D_n)处稳态队长分布的重要关系(不同于连续时间排队系统). 相似文献
6.
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
7.
Abstract In this article, we study a queueing system M x /G/1 with multiple vacations. The probability generating function (P.G.F.) of stationary queue length and its expectation expression are deduced by using an embedded Markov chain of the queueing process. The P.G.F. of stationary system busy period and the probability of system in service state and vacation state also are obtained by the same method. At last we deduce the LST and mean of stationary waiting time in the service order FCFS and LCFS, respectively. 相似文献
8.
This paper examines an M[x]/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1-p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the J th vacation, the server is dormant idly in the system. If there is one or more customers arrive at server idle state, the server immediately starts his services for the arrivals. For such a system, we derive the distributions of important characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, idle period and busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p∗,J∗) at a minimum cost, and some numerical examples are presented for illustrative purpose. 相似文献
9.
This paper studies the operating characteristics of an M[x]/G/1 queueing system under a variant vacation policy, where the server leaves for a vacation as soon as the system is empty. The server takes at most J vacations repeatedly until at least one customer is found waiting in the queue when the server returns from a vacation. If the server is busy or on vacation, an arriving batch balks (refuses to join) the system with probability 1 − b. We derive the system size distribution at different points in time, as well as the waiting time distribution in the queue. Finally, important system characteristics are derived along with some numerical illustration. 相似文献
10.
B. Krishna Kumar D. Arivudainambi A. Krishnamoorthy 《Annals of Operations Research》2006,143(1):277-296
This paper deals with a generalized M/G/1 feedback queue in which customers are either “positive" or “negative". We assume that the service time distribution of
a positive customer who initiates a busy period is G
e
(x) and all subsequent positive customers in the same busy period have service time drawn independently from the distribution
G
b
(x). The server is idle until a random number N of positive customers accumulate in the queue. Following the arrival of the N-th positive customer, the server serves exhaustively the positive customers in the queue and then a new idle period commences.
This queueing system is a generalization of the conventional N-policy queue with N a constant number. Explicit expressions for the probability generating function and mean of the system size of positive customers
are obtained under steady-state condition. Various vacation models are discussed as special cases. The effects of various
parameters on the mean system size and the probability that the system is empty are also analysed numerically.
AMS Subject Classification: Primary: 60 K 25 · Secondary: 60 K 20, 90 B 22 相似文献
11.
We consider aM
X/G/1 queueing system withN-policy. The server is turned off as soon as the system empties. When the queue length reaches or exceeds a predetermined valueN (threshold), the server is turned on and begins to serve the customers. We place our emphasis on understanding the operational characteristics of the queueing system. One of our findings is that the system size is the sum of two independent random variables: one has thePGF of the stationary system size of theM
X/G/1 queueing system withoutN-policy and the other one has the probability generating function
j=0
N=1
j
z
j/
j=0
N=1
j
, in which j is the probability that the system state stays atj before reaching or exceedingN during an idle period. Using this interpretation of the system size distribution, we determine the optimal thresholdN under a linear cost structure. 相似文献
12.
We study a multi-server M/M/c type queue with a single vacation policy for some idle servers. In this queueing system, if at a service completion instant, any d (d c) servers become idle, these d servers will take one and only one vacation together. During the vacation of d servers, the other c–d servers do not take vacation even if they are idle. Using a quasi-birth-and-death process and the matrix analytic method, we obtain the stationary distribution of the system. Conditional stochastic decomposition properties have been established for the waiting time and the queue length given that all servers are busy. 相似文献
13.
14.
Yixin Zhu 《Queueing Systems》1991,8(1):255-263
We study anM/M/1 group arrival queue in which the arrival rate, service time distributions and the size of each group arrival depend on
the state of an underlying finite-state Markov chain. Using Laplace transforms and matrix analysis, we derive the results
for the queue length process, its limit distribution and the departure process. In some special cases, explicit results are
obtained which are analogous to known classic results. 相似文献
15.
16.
We consider an M X /G/1 queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under a linear retrial policy. In addition, each individual customer is subject to a control admission policy upon the arrival. This model generalizes both the classical M/G/1 retrial queue with arrivals in batches and a two phase batch arrival queue with a single vacation under Bernoulli vacation schedule. We will carry out an extensive stationary analysis of the system , including existence of the stationary regime, embedded Markov chain, steady state distribution of the server state and number of customer in the retrial group, stochastic decomposition and calculation of the first moment. 相似文献
17.
We consider finite buffer single server GI/M/1 queue with exhaustive service discipline and multiple working vacations. Service times during a service period, service times during a vacation period and vacation times are exponentially distributed random variables. System size distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system etc. have been obtained. The model has potential application in the area of communication network, computer systems etc. where a single channel is allotted for more than one source. 相似文献
18.
We consider a finite buffer batch service queueing system with multiple vacations wherein the input process is Markovian arrival
process (MAP). The server leaves for a vacation as soon as the system empties and is allowed to take repeated (multiple) vacations. The
service- and vacation- times are arbitrarily distributed. We obtain the queue length distributions at service completion,
vacation termination, departure, arbitrary and pre-arrival epochs. Finally, some performance measures such as loss probability,
average queue lengths are discussed. Computational procedure has been given when the service- and vacation- time distributions
are of phase type (PH-distribution). 相似文献
19.
Hideaki Takagi 《Queueing Systems》1990,6(1):369-389
We analyze the time-dependent process in severalM/G/1 vacation models, and explicitly obtain the Laplace transform (with respect to an arbitrary point in time) of the joint
distribution of server state, queue size, and elapsed time in that state. Exhaustive-serviceM/G/1 systems with multiple vacations, single vacations, an exceptional service time for the first customer in each busy period,
and a combination ofN-policy and setup times are considered. The decomposition property in the steady-state joint distribution of the queue size
and the remaining service time is demonstrated. 相似文献
20.
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