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61.
We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the
second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review
since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different
kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit
ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically
and optimal thresholds that yield minimum cost are sought. 相似文献
62.
In this paper a multi-server queueing model with Markovian arrivals and synchronous phase type vacations is studied using a probabilistic rule and controlled thresholds. The steady-state analysis of the model is presented. An optimization problem and some interesting numerical results are discussed. 相似文献
63.
Gautam Choudhury 《TOP》2003,11(1):141-150
This paper examines the steady state behaviour of anM/G/1 queue with a second optional service in which the server may provide two phases of heterogeneous service to incoming units.
We derive the queue size distribution at stationary point of time and waiting time distribution. Moreover we derive the queue
size distribution at the departure point of time as a classical generalization of the well knownPollaczek Khinchin formula. This is a generalization of the result obtained by Madan (2000).
This work is supported by Department of Atomic Energy, Govt. of India, NBHM Project No. 88/2/2001/R&D II/2001. 相似文献
64.
The object of this research in queueing theory is the Law of the Iterated Logarithm (LIL) under the conditions of heavy traffic
in Multiphase Queueing Systems (MQS). In this paper, the LIL is proved for extreme values of important probabilistic characteristics
of the MQS investigated as well as maxima and minima of the summary queue length of customers and maxima and minima of the
queue length of customers. Also, the paper presents a survey on the works for extreme values in queues and the queues in heavy
traffic.
相似文献
65.
Tsung-Yin Wang Jau-Chuan Ke Kuo-Hsiung Wang Siu-Chuen Ho 《Mathematical Methods of Operations Research》2006,63(2):371-384
This paper studies maximum likelihood estimates as well as confidence intervals of an M/M/R queue with heterogeneous servers under steady-state conditions. We derive the maximum likelihood estimates of the mean arrival rate and the three unequal mean service rates for an M/M/3 queue with heterogeneous servers, and then extend the results to an M/M/R queue with heterogeneous servers. We also develop the confidence interval formula for the parameter ρ, the probability of empty system P
0, and the expected number of customers in the system E[N], of an M/M/R queue with heterogeneous servers 相似文献
66.
This paper studies the vacation policies of an M/G/1 queueing system with server breakdowns, startup and closedown times, in which the length of the vacation period is controlled either by the number of arrivals during the vacation period, or by a timer. After all the customers are served in the queue exhaustively, the server is shutdown (deactivates) by a closedown time. At the end of the shutdown time, the server immediately takes a vacation and operates two different policies: (i) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or the waiting time of the leading customer reaches T units; and (ii) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the closedown time. If the timer expires or the number of arrivals exceeds the threshold N, then the server reactivates and requires a startup time before providing the service until the system is empty. If some customers arrive during this closedown time, the service is immediately started without leaving for a vacation and without a startup time. We analyze the system characteristics for each scheme. 相似文献
67.
We study the steady-state queue length and waiting time of the M/G/1 queue under the D-policy and multiple server vacations. We derive the queue length PGF and the LSTs of the workload and waiting time. Then,
the mean performance measures are derived. Finally, a numerical example is presented and the effects of employing the D-policy are discussed.
AMS Subject Classifications 60K25
This work was supported by the SRC/ERC program of MOST/KOSEF grant # R11-2000-073-00000. 相似文献
68.
We consider queueing systems in which the server occasionally takes a vacation of random duration. The vacation can be used
to do additional work; it can also be a rest period. Several models of this problem have been analyzed in the past assuming
that the population of the system is infinite. Similarly, it is generally assumed that the capacity of the system is infinite.
In this paper we show how the finite-population system can be modeled by the stochastic Petri net. We also extend the model
to the finite-capacity system.
This research was sponsored by the SDIO Innovative Science and Technology Office and was managed by the Office of Naval Research
under grant N3014-88-K-0623. 相似文献
69.
In this paper, we study the total sojourn time in a queueing system with an instantaneous tri-route decision process. Even though the computations are more difficult, we give here the structure of the sojourn time process for the M/G/1 queue with tri-route decision process. A numerical study is carried out in this paper. 相似文献
70.
This paper discusses an optimal age maintenance scheme for a queueing system. Customers arrive at the system according to a Poisson process. They form a single queue and are served by a server with general service distribution. The system fails after a random time and corrective maintenance is performed at the failure. A preventive maintenance is also performed if the system is empty at age T where ‘age’ refers to the elapsed time since the previous maintenance was completed. If the system is not empty at age T, the system is used until it fails. At the failure, the customers in the system are lost and the arriving customers during the maintenance are also lost. By renewal theory, we study the optimal value of T which minimizes the average number of lost customers over an infinite time horizon. 相似文献