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1.
We obtain the sojourn time probability distribution function at equilibrium for a Markov modulated, multi-server, single queue with generalised exponential (GE) service time distribution and compound Poisson arrivals of both positive and negative customers. Such arrival processes can model both burstiness and correlated traffic and are well suited to models of ATM and other telecommunication networks. Negative customers remove (ordinary) customers in the queue and are similarly correlated and bursty. We consider both the cases where negative customers remove positive customers from the front and the end of the queue and, in the latter case, where a customer currently being served can and cannot be killed by a negative customer. These cases can model an unreliable server or load balancing respectively. The results are obtained as Laplace transforms and can be inverted numerically. The MM CPP/GE/c G-Queue therefore holds the promise of being a viable building block for the analysis of queues and queueing networks with bursty, correlated traffic, incorporating load balancing and node-failures, since the equilibrium behaviour of both queue lengths and response times can be determined in a tractable way. 相似文献
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In queueing theory, most models are based on time-homogeneous arrival processes and service time distributions. However, in communication networks arrival rates and/or the service capacity usually vary periodically in time. In order to reflect this property accurately, one needs to examine periodic rather than homogeneous queues. In the present paper, the periodic BMAP/PH/c queue is analyzed. This queue has a periodic BMAP arrival process, which is defined in this paper, and phase-type service time distributions. As a Markovian queue, it can be analysed like an (inhomogeneous) Markov jump process. The transient distribution is derived by solving the Kolmogorov forward equations. Furthermore, a stability condition in terms of arrival and service rates is proven and for the case of stability, the asymptotic distribution is given explicitly. This turns out to be a periodic family of probability distributions. It is sketched how to analyze the periodic BMAP/M
t
/c queue with periodically varying service rates by the same method. 相似文献
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We study the departure process of a single server queue with Markovian arrival input and Markov renewal service time. We derive the joint transform of departure time and the number of departures and, based on this transform, we establish several expressions for burstiness (variance) and correlation (covariance sequence) of the departure process. These expressions reveal that burstiness and correlation of the arrival process have very little impact on the departure process when a queueing system is heavily loaded. In contrast, both burstiness and correlation of the service-time process greatly affect those of the departure process regardless of the load of the system. Finally, we show that, even when an arrival process is short-range dependent, the departure process could has long-range dependence if a service-time process is long-range dependent. 相似文献
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利用了概率论中的弱极限定理,研究了服务中断的带优先反馈排队系统弱极限定理,得到了队长,虚等待时间及逗留时间的弱极限定理. 相似文献
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A discrete-time system of a tandem of queues with exogenous arrivals and departures at each stage is considered. A customer leaving queuek–1 departs the system with probability 1–
[k]
and continues to queuek with probability
[k]
. Exogenous arrivals to each stage are i.i.d. at each time slot. An approximate analysis of the occupancy and busy-period distributions of each stage based on a General Busy-period with batches and Memoryless (geometric) Idle period renewal Process (GBMIP) provides improved performance over two-state Markov approximations and gives exact results when there are no interstage departures.This research was supported in part by NSF grant NCR-8708282. 相似文献
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多重休假的带启动期Geom/G/1排队 总被引:9,自引:2,他引:9
本文研究多重休假的带启动期的Geom/G/1离散时间排队。给出稳态队长,等待时间分布的母函数及其随机分解结果,推导出忙期,假期和启动期的母函数等。 相似文献
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Yuan Yuan LIU Zhen Ting HOU 《数学学报(英文版)》2007,23(7):1289-1296
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
12.
In this paper an analysis of the output process from an M/M/1 queue where the arrival and service rates vary randomly is presented. The results include expressions for the mean, variance and distribution of the interdeparture interval, the joint density function of two successive interdeparture intervals and their correlation. An interesting feature of the results is that the moments of the interdeparture time are expressed in terms of the expected times to first and second departures from an arbitrary point in time. 相似文献
13.
Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue 总被引:2,自引:0,他引:2
We are concerned with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. It is known that an analytical solution of this queueing model is difficult and does not lead to numerical implementation. Based on appropriate understanding of the physical behavior, an efficient and numerically stable algorithm for computing the stationary distribution of the system state is developed. Numerical calculations are done to compare our approach with the existing approximations. 相似文献
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This paper considers the delay distributions in a two-class non-preemptive priority queue with crossover feedback. Specifically, there are two priority classes, and the Poisson arrival process for each class can be subdivided into two groups: one group which only requires service at the priority level to which it arrives, and another group which requires subsequent service after it feeds back to the other queue. Our main result is the determination of explicit expressions for the distribution of delay until final service commences for each the four types of customers. 相似文献
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利用有限状态拟生灭过程和全概率分解的方法,首次研究了只允许部分服务台同步多重休假的M/M/e/k排队系统,得到了稳态队长和等待时间分布,并且讨论了系统的优化问题. 相似文献
17.
D.J. Daley 《Stochastic Processes and their Applications》1975,3(2):185-191
The Laplace-Stieltjes transform of the variance function V(y) = var (N(0, y]) for the number N(0, y] of departures in a time interval of length y is found for stationary M/G/1 and G1/M/1 queueing systems. It is shown that for G1/M/1 systems V(y) is linear only for M/M/1. 相似文献
18.
Under light traffic, we investigate the quality of a well‐known approximation for first‐moment performance measures for an
M/G/c queue, and, in particular, conditions under which the approximation is either an upper or a lower bound. The approach is
to combine known relationships between quantities such as average delay and time‐average work in system with direct sample‐path
comparisons of system operation under two modes of operation: conventional FIFO and a version of preemptive LIFO. We then
use light traffic limit theorems to show an inequality between time‐average work of the M/G/c queue and that of the approximation. In the process, we obtain new and improved approximations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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对负顾客进行服务的M/GI/1模型的稳态队长 总被引:4,自引:0,他引:4
本文基于配套加工零件的应用实例,提出了一个新的负顾客排队模型,利用补充变量法和状态转移分析,得到了稳态下队长分布的带负幂的母函数表达式。 相似文献
20.
Closed-form relations are derived for the probabilities and performance measures observed at random/arrival/departure epochs in a multi-server queue with group arrivals. 相似文献