共查询到10条相似文献,搜索用时 125 毫秒
1.
Consider a single-server queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establish that this system can be approximated by either a reflected Ornstein–Uhlenbeck process or a reflected affine diffusion when the arrival rate exceeds or is close to the processing rate and the reneging rate is close to 0. We further compare the quality of the steady-state distribution approximations suggested by each diffusion. 相似文献
2.
Yong-jiang Guo 《应用数学学报(英文版)》2011,27(1):43-58
A GI/G/1 queue with vacations is considered in this paper.We develop an approximating technique on max function of independent and identically distributed(i.i.d.) random variables,that is max{ηi,1 ≤ i ≤ n}.The approximating technique is used to obtain the fluid approximation for the queue length,workload and busy time processes.Furthermore,under uniform topology,if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate,we prove by the... 相似文献
3.
The arrival of a negative customer to a queueing system causes one positive customer to be removed if any is present. Continuous-time queues with negative and positive customers have been thoroughly investigated over the last two decades. On the other hand, a discrete-time Geo/Geo/1 queue with negative and positive customers appeared only recently in the literature. We extend this Geo/Geo/1 queue to a corresponding GI/Geo/1 queue. We present both the stationary queue length distribution and the sojourn time distribution. 相似文献
4.
We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system
workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer
content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order
linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve
them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical
examples.
相似文献
5.
Wen-Hui Zhou 《Applied mathematics and computation》2005,170(2):1349-1355
In this paper, we consider a discrete-time GI/G/1 queueing model with negative arrivals. By deriving the probability generating function of actual service time of ordinary customers, we reduced the analysis to an equivalent discrete-time GI/G/1 queueing model without negative arrival, and obtained the probability generating function of buffer contents and random customer delay. 相似文献
6.
Analysis of a GI/M/1 queue with multiple working vacations 总被引:3,自引:0,他引:3
Yutaka Baba 《Operations Research Letters》2005,33(2):201-209
Consider a GI/M/1 queue with vacations such that the server works with different rates rather than completely stops during a vacation period. We derive the steady-state distributions for the number of customers in the system both at arrival and arbitrary epochs, and for the sojourn time for an arbitrary customer. 相似文献
7.
We consider an M/PH/1 queue with balking based on the workload. An arriving customer joins the queue and stays until served only if the system
workload is below a fixed level at the time of arrival. The steady state workload distribution in such a system satisfies
an integral equation. We derive a differential equation for Phase type service time distribution and we solve it explicitly,
with Erlang, Hyper-exponential and Exponential distributions as special cases. We illustrate the results with numerical examples. 相似文献
8.
In this paper we consider the problem of controlling the arrival of customers into a GI/M/1 service station. It is known that when the decisions controlling the system are made only at arrival epochs, the optimal acceptance strategy is of a control-limit type, i.e., an arrival is accepted if and only if fewer than n customers are present in the system. The question is whether exercising conditional acceptance can further increase the expected long run average profit of a firm which operates the system. To reveal the relevance of conditional acceptance we consider an extension of the control-limit rule in which the nth customer is conditionally admitted to the queue. This customer may later be rejected if neither service completion nor arrival has occurred within a given time period since the last arrival epoch. We model the system as a semi-Markov decision process, and develop conditions under which such a policy is preferable to the simple control-limit rule. 相似文献
9.
We consider a batch arrival finite buffer single server queue with inter-batch arrival times are generally distributed and
arrivals occur in batches of random size. The service process is correlated and its structure is presented through Markovian
service process (MSP). The model is analyzed for two possible customer rejection strategies: partial batch rejection and total batch rejection
policy. We obtain steady-state distribution at pre-arrival and arbitrary epochs along with some important performance measures,
like probabilities of blocking the first, an arbitrary, and the last customer of a batch, average number of customers in the
system, and the mean waiting times in the system. Some numerical results have been presented graphically to show the effect
of model parameters on the performance measures. The model has potential application in the area of computer networks, telecommunication
systems, manufacturing system design, etc.
相似文献
10.
Consider a GI/M/1 queue with start-up period and single working vacation. When the system is in a closed state, an arriving customer leading to a start-up period, after the start-up period, the system becomes a normal service state. And during the working vacation period, if there are customers at a service completion instant, the vacation can be interrupted and the server will come back to the normal working level with probability p (0 ? p ? 1) or continue the vacation with probability 1 − p. Meanwhile, if there is no customer when a vacation ends, the system is closed. Using the matrix-analytic method, we obtain the steady-state distributions for the queue length at both arrival epochs and arbitrary epochs, the waiting time and sojourn time. 相似文献