首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 78 毫秒
1.
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   

2.
THE DECOMPOSITION OF STATE SPACE FOR MARKOV CHAIN IN RANDOM ENVIRONMENT   总被引:2,自引:1,他引:1  
This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random walk in random environment, renewal process in random environment and queue process in random environment, and obtains the decompositions of the state spaces of these three special examples.  相似文献   

3.
This paper investigates the explicit convergence rates to the stationary distribution π of the embedded M/G/1 queue; specifically, for suitable rate functions r(n) which may be polynomial with r(n) = n^l, l 〉 0 or geometric with r(n) = α^n, a 〉 1 and "moments" f ≥ 1, we find the conditions under which Σ∞n=0 r(n)||P^n(i,·) - π(·)||f ≤ M(i) for all i ∈ E. For the polynomial case, the explicit bounds on M(i) are given in terms of both "drift functions" and behavior of the first hitting time on the state O; and for the geometric case, the largest geometric convergence rate α* is obtained.  相似文献   

4.
In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric(parameter p) distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method (techniques of probability decomposition, renewal process theory) that is different from the techniques used by Hunter(1983), the transient property of the queue with initial state i(i ≥ 0) is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^+ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.  相似文献   

5.
We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.  相似文献   

6.
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   

7.
This paper considers an on-off fluid queue model. The on and off states of the system appear alternately, and the sojourn times at these two different states are independent, and each one follows an exponential distribution. The fluid flows into the system buffer with some strategies to wait for the system service under the first-come first-served discipline. Here the system can process the fluid in the buffer only when the system is on state. With given utility functions such as an expected ave...  相似文献   

8.
In this paper, we consider a discrete-time preemptive priority queue with different service completion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers’ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuoustime model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.  相似文献   

9.
10.
M/G/1 QUEUE WITH CONTROLLABLE VACATIONS AND OPTIMIZATION OF VACATION POLICY   总被引:1,自引:0,他引:1  
We introduce the control parameter N in a common queue M/G/1 with vacations; the endof a global vacation period is controlled by the parameter N. Thia extension for a queue withvacations is of significance in certain practical cases. In this paper, we find various transient andsteady-state results for the queue size. the delay times and the waiting times for the M/G/1 queuewith controllable vacations. Finally, we also discuss optimal selection of the control parameter.  相似文献   

11.
Polling systems and multitype branching processes   总被引:8,自引:3,他引:5  
The joint queue length process in polling systems with and without switchover times is studied. If the service discipline in each queue satisfies a certain property it is shown that the joint queue length process at polling instants of a fixed queue is a multitype branching process (MTBP) with immigration. In the case of polling models with switchover times, it turns out that we are dealing with an MTBP with immigration in each state, whereas in the case of polling models without switchover times we are dealing with an MTBP with immigration in state zero. The theory of MTBPs leads to expressions for the generating function of the joint queue length process at polling instants. Sufficient conditions for ergodicity and moment calculations are also given.This work was done while the author was at the Centre for Mathematics and Computer Science (CWI) in Amsterdam, The Netherlands.  相似文献   

12.
We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

13.
The IP P+M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L(t)for IP P+M/M/1 queue has been proved in[10].In this paper,we shall give the su?cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.  相似文献   

14.
李锐  侯振挺 《经济数学》2004,21(2):161-167
侯振挺、李晓花在 [1]已经讨论了具有某些特殊形式的拟生灭过程各种遍历性 ,我们将在此基础讨论一般形式连续时间拟生灭过程各种遍历性 ,并给出 [1]中连续时间拟生灭过程的指数遍历及多项式遍历的一个新证明 ,该证明给出了具有某些特殊条件下连续时间拟生灭过程遍历性与离散时间拟生灭过程遍历性之间关系 .  相似文献   

15.
A Markov polling system with infinitely many stations is studied. The topic is the ergodicity of the infinite-dimensional process of queue lengths. For the infinite-dimensional process, the usual type of ergodicity cannot prevail in general and we introduce a modified concept of ergodicity, namely, weak ergodicity. It means the convergence of finite-dimensional distributions of the process. We give necessary and sufficient conditions for weak ergodicity. Also, the “usual” ergodicity of the system is studied, as well as convergence of functionals which are continuous in some norm. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

16.
Consider a number of parallel queues, each with an arbitrary capacity and multiple identical exponential servers. The service discipline in each queue is first-come-first-served (FCFS). Customers arrive according to a state-dependent Poisson process. Upon arrival, a customer joins a queue according to a state-dependent policy or leaves the system immediately if it is full. No jockeying among queues is allowed. An incoming customer to a parallel queue has a general patience time dependent on that queue after which he/she must depart from the system immediately. Parallel queues are of two types: type 1, wherein the impatience mechanism acts on the waiting time; or type 2, a single server queue wherein the impatience acts on the sojourn time. We prove a key result, namely, that the state process of the system in the long run converges in distribution to a well-defined Markov process. Closed-form solutions for the probability density function of the virtual waiting time of a queue of type 1 or the offered sojourn time of a queue of type 2 in a given state are derived which are, interestingly, found to depend only on the local state of the queue. The efficacy of the approach is illustrated by some numerical examples.  相似文献   

17.
分析了一个带有负顾客、N-策略控制的Geo/Geo/1多重工作休假排队系统, 其中正顾客在工作休假及正规忙期以不同的到达率进入系统. 利用拟生灭过程和矩阵几何解方法, 给出了该模型的稳态队长分布及平均队长, 以及系统分别处于假期和忙期的概率. 同时, 对该系统的忙期进行了分析, 并讨论了稳态队长分布在系统容量的优化设计中的应用. 最后, 在给定的费用结构下, 用数值计算例子确定了使系统长期单位时间内期望费用最小的最优控制策 N*.  相似文献   

18.
19.
N策略工作休假M/M/1排队   总被引:4,自引:0,他引:4  
考虑策略工作休假M/M/1排队,简记为M/M/1(N-WV)。在休假期间,服务员并未完全停止工作而是以较低的速率为顾客服务。用拟生灭过程和矩阵几何解方法,我们给出了有直观概率意义的稳态队长和稳态条件等待时间的分布。此外,我们也得到了队长和等待时间的条件随机分解结构及附加队长和附加延迟的分布。  相似文献   

20.
M/G/1非空竭服务休假排队系统的平衡条件分析   总被引:2,自引:0,他引:2  
讨论了一般非空竭服务M/G/1型休假排队系统的嵌入更新过程常返的条件,为稳态队长与等待时间的随机分解奠定理论基础.并且在独立休假策略下进一步简化Fuhrman与Cooper(1985)休假排队系统的随机分解的条件,并得到完整的随机分解结构.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号