PH/PH/1/N反馈排队系统的逗留时间

具有反馈依赖于队长的PH／PH／1／N排队系统的队长和忙期的研究已在文[1]中解决，本文主要解决本系统的逗留时间的研究．     

具有不耐烦顾客和PH分布休假的M/M/1排队系统

研究了具有不耐烦顾客的M/M/1休假排队系统,其中休假时间服从位相分布.当顾客在休假时间到达系统,顾客则会因为等待变得不耐烦.服务员休假结束后立刻开始工作.如果在顾客不耐烦时间段内,系统的休假还没有结束,顾客就会离开系统不再回来.建立的模型为水平相依QBD拟生灭过程,通过利用BrightTaylor算法得到系统的稳态概率解.同时还得到一些重要的性能指标.最后通过数据实例验证了我们的结论.     

Geometric/G/1离散时间可修排队系统

研究服务台可修的Geomertric/G/1离散时间排队系统.在这个系统中,服务台寿命服从几何分布,修理时间服从一般分布.我们求出了服务台首次故障前时间的母函数和服务台首次故障前平均时间(MTTFF).     

带启动时间的多级适应性休假的M/G/1排队

本研究带启动时间的多级适应性休假的M/G/1间排队。给出稳态队长分布和母函数、等待时间分布和其LST及其随机分解结果，推导出忙期、假期和启动期的母函数。带有启动时间的单重休假和多重休假是本中模型的两个极端情况。     

M/M/c休假排队系统稳态分布的数值计算

从数值计算角度研究M/M/c休假排队系统稳定状态的概率分布.采用GMRES方法求解概率分布向量所满足的大型线性方程,构造了一个循环预处理算子加速GMRES方法的收敛.数值实例验证了该算法的优越性.     

休假时间服从T-SPH分布的M/M/1多重休假排队

本文研究休假时间服从T-SPH分布的M/M/1多重休假排队,利用拟生灭过程和算子几何解的方法给出了平稳队长分布的概率母函数,并得到了平稳队长和平稳等待时间的随机分解结果以及附加队长和附加延迟的母函数和LST的具体形式.     

服务台休假的GI/Geom/1离散时间排队

本文研究了具有位相型休假、位相型启动和单重几何休假的离散时间排队,假定 顾客到达间隔服从一般分布,服务时间服从几何分布,运用矩阵解析方法我们得到了这 些排队系统中顾客在到达时刻稳态队长分布及其随机分解.     

具有可选服务、反馈、一般重试时间的M/G/1排队系统

本文考虑了一个具有可选服务、反馈的M／G／1重试排队系统。在假定重试区域中只有队首的顾客允许重试的情况下，重试时间具有一般分布时，得到了系统稳态的充分必要条件。求得稳态时系统队长和重试区域中队长分布及相关指标。     

对M/T-SPH/1排队平稳指标的进一步研究—数值计算与渐近分析

讨论M/T-SPH/1排队平稳队长分布的数值计算,以及平稳队长和逗留时间分布各阶矩的数值计算及渐近分析.其中T-SPH表示可数状态吸收生灭链吸收时间的分布.在分布PGF和LST的基础上,首先给出了计算平稳队长分布,平稳队长以及逗留时间分布各阶矩的数值结果的递推公式.其次还讨论了平稳队长及平稳逗留时间分布各阶矩的尾部渐近...     

单重休假闸门服务的Geom/G/1离散时间排队系统

文章研究了单重休假的Geom/G/1闸门服务系统,推导出稳态下系统队长的母函数,FCFS规则下的等待时间的母函数,使用离散时间队长和剩余工作量的分解性质,求出剩余工作量的母函数,最后给出服务周期的性能指标的母函数,及系统处在各种状态的概率.     

The conditional sojourn time distribution in the GI/M/1 processor-sharing queue in heavy traffic

We treat the GI/M/1 queue with a processor-sharing server, in the heavy traffic case. Using perturbation methods, we construct asymptotic expansions for the conditional sojourn time distribution of a tagged customer conditioned on the tagged customer's service time. The resulting approximation is simple in form and involves only the first three moments of the interarrival time distribution.     

Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not suitable for computational purposes. This paper derives readily applicable insensitive bounds for all moments of the conditional sojourn time distribution. The instantaneous sojourn time, i.e., the sojourn time of an infinitesimally small job, leads to insensitive upper bounds requiring only knowledge of the traffic intensity and the initial job size. Interestingly, the upper bounds involve polynomials with so-called Eulerian numbers as coefficients. In addition, stochastic ordering and moment ordering results for the sojourn time distribution are obtained. AMS Subject Classification: 60K25, 60E15 This work has been partially funded by the Dutch Ministry of Economic Affairs under the program ‘Technologische Samenwerking ICT-doorbraakprojecten’, project TSIT1025 BEYOND 3G.     

On the average sojourn time under M/M/1/SRPT

We study an M/M/1 queueing system under the shortest remaining processing time (SRPT) policy. We show that the average sojourn time varies as , where ρ is the system load. Thus, SRPT offers a Θ(ln(e/(1−ρ))) factor improvement over policies that ignore knowledge of job sizes while scheduling.     

Sojourn time asymptotics in the M/G/1 processor sharing queue

We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index -ν, ν non-integer, iff the sojourn time distribution is regularly varying of index -ν. This result is derived from a new expression for the Laplace–Stieltjes transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution. We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojourn time distribution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic limiting sojourn time distribution when the service time distribution is regularly varying. Explicit formulas and multiterm expansions are provided for the case that the service time has a Pareto distribution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Sojourn time distribution in a MAP/M/1 processor-sharing queue

This paper considers the sojourn time distribution in a processor-sharing queue with a Markovian arrival process and exponential service times. We show a recursive formula to compute the complementary distribution of the sojourn time in steady state. The formula is simple and numerically feasible, and enables us to control the absolute error in numerical results. Further, we discuss the impact of the arrival process on the sojourn time distribution through some numerical examples.     

Asymptotic expansions for the sojourn time distribution in the M/G/1-PS queue

We consider the M/G/1 queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer’s service requirement, as well as the unconditional distribution, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. Our results demonstrate the possible tail behaviors of the unconditional distribution, which was previously known in the cases G = M and G = D (where it is purely exponential). We assume that the service density decays at least exponentially fast. We use various methods for the asymptotic expansion of integrals, such as the Laplace and saddle point methods.     

Remarks on the remaining service time upon reaching a target level in the M/G/1 queue

In this note we establish connections between new and previous results on the remaining service time upon reaching a target level in the M/G/1 queue.     

Joint distribution of sojourn time and queue length in the M/G/1 queue with (in) finite capacity

For the M/G/1 queue we study the joint distribution of the number of customers x present immediately before an arrival epoch and of the residual service time ζ of the customer in service at this epoch. The correlation coefficient ? (x, ζ) is shown to be positive (negative) when the service time distribution is DFR (IFR). The result for the joint distribution of x and ζ leads to the joint distribution of x, of the sojourn time s of the arriving customer and of the number of customers z left behind by this customer at his departure. ?(x, s), ?(z, s) and ?(x, z) are shown to be positive; ?(x, s) and ?(z, s) are compared in some detail.Subsequently the M/G/1 queue with finite capacity is considered; the joint distributions of x and ζ and of x and s are derived. These results may be used to study the cycle time distribution in a two-stage cyclic queue.     

Stationary distribution of queue length in G / M / 1 queue with two-stage service policy

We consider a G / M / 1 queue with two-stage service policy. The server starts to serve with rate of μ₁ customers per unit time until the number of customers in the system reaches λ. At this moment, the service rate is changed to that of μ₂ customers per unit time and this rate continues until the system is empty. We obtain the stationary distribution of the number of customers in the system.     

Heavy-traffic analysis of the sojourn time in a three node Jackson network with overtaking

We consider a Jackson network consisting of three first-in-first-out (FIFO)M/M/1 queues. When customers leave the first queue they can be routed to either the second or third queue. Thus, a customer that traverses the network by going from the first to the second to the third queue, can be overtaken by another customer that is routed from the first queue directly to the third. We study the distribution of the sojourn time of a customer through the three node network, in the heavy traffic limit. A three term heavy traffic asymptotic approximation to the sojourn time density is derived. The leading term shows that the nodes decouple in the heavy traffic limit. The next two terms, however, do show the dependence of the sojourn times at the individual nodes and give quantitative measures of the effects of overtaking.