The Interarrival Hyperexponential Queues:Hk/M/c/N With Balking And Reneging

This paper treats the analytical solution of the truncated interarrival hyperexponential queue. H_k/M/c/N with balking and reneging for general values of k,c and N. The discipline considered here is FIFO. Some previously published results are shown to be special cases of the present results     

A production system with two job classes,changeover times and revisitation

This paper, motivated by the need to predict performance of production systems with random arrivals, setup times and revisitation, presents an imbedded Markov chain analysis of the underlyingM/G/1 queue with two customer classes, changeover times and instantaneous Bernoulli feedback. It is assumed that jobs are scheduled according to the exhaustive alternative priority queue discipline. Expressions for the mean waiting time and the nonsaturation condition are derived under two different priority assignments to the repeat customers. Sojourn times under these priority assignments are shown to possess a convex ordering. Results of the study are also applicable to data communication networks that operate under cyclic switching mechanisms. Research supported in part by Natural Sciences and Engineering Research Council of Canada.     

A survey of retrial queues

We present a survey of the main results and methods of the theory of retrial queues, concentrating on Markovian single and multi-channel systems. For the single channel case we consider the main model as well as models with batch arrivals, multiclasses, customer impatience, double connection, control devices, two-way communication and buffer. The stochastic processes arising from these models are considered in the stationary as well as the nonstationary regime. For multi-channel queues we survey numerical investigations of stationary distributions, limit theorems for high and low retrial intensities and heavy and light traffic behaviour.     

The M/G/1 retrial queue with bernoulli schedule

We consider anM/G/1 retrial queue with infinite waiting space in which arriving customers who find the server busy join either (a) the retrial group with probabilityp in order to seek service again after a random amount of time, or (b) the infinite waiting space with probabilityq(=1–p) where they wait to be served. The joint generating function of the numbers of customers in the two groups is derived by using the supplementary variable method. It is shown that our results are consistent with known results whenp=0 orp=1.     

On computing average cost optimal policies with application to routing to parallel queues

The Approximating Sequence Method for computation of average cost optimal stationary policies in denumerahle state Markov decision chains, introduced in Sennott (1994), is reviewed. New methods for verifying the assumptions are given. These are useful for models with multidimensional state spaces that satisfy certain mild structural properties. The results are applied to four problems in the optimal routing of packets to parallel queues. Numerical results are given for one of the models.     

Some analytical results for congestion in subscriber line modules

In modern telephone exchanges, subscriber lines are usually connected to the so-called subscriber line modules. These modules serve both incoming and outgoing traffic. An important difference between these two types of calls lies in the fact that in the case of blocking due to all channels busy in the module, outgoing calls can be queued whereas incoming calls get busy signal and must be re-initiated in order to establish the required connection. The corresponding queueing model was discussed recently by Lederman, but only the model with losses has been studied analytically. In the present contribution, we study the model which takes into account subscriber retrials and investigate some of its properties such as existence of stationary regime, derive explicit formulas for the system characteristics, limit theorems for systems under high repetition intensity of blocked calls and limit theorems for systems under heavy traffic.     

A duality approach to admission and scheduling controls of queues

This paper studies theadmission andscheduling control problem in anM/M/2 queueing system with nonidentical processors. Admission control renders when a newly arrived job should be accepted, whereas scheduling control determines when an available processor should be utilized. The system received a rewardR when a job completes its service and pays a unit holding costC while a job is in the system. The main goal of the paper is to obtain the admission/scheduling policy that maximizes the expected discounted and long-run average profits (reward minus cost). We convert the system into its dual, a stochastically identical system subject toexpulsion/scheduling control, and prove that the individually optimal policy in the dual system is socially optimal in the original system. In contrast with the dynamic programming (DP) technique which considers the system as a whole, we adopt the viewpoint of an individual job and analyze the impact of its behavior on the social outcome. The key properties which simplify the analysis are that under the individually optimal policy the profit of a job under the preemptive last-come first-priority service discipline (LCFP-P) is independent of jobs arrived earlier than itself and that the system is insensitive to service discipline imposed. The former makes possible to bypass complex dynamic programming analyses and the latter serves as a vehicle in connecting the social and individual optimality. We also exploit system operational characteristics under LCFP-P to obtain simple and close approximations of the optimal thresholds.     

频率模型与一个考古问题

本文给出了式样流行的几何频率模型 ,并用该数学模型解决了考古学中确定发掘物先后历史年代的问题 .     

Closed queueing networks with batch services

In this paper we study queueing networks which allow multiple changes at a given time. The model has a natural application to discrete-time queueing networks but describes also queueing networks in continuous time. It is shown that product-form results which are known to hold when there are single changes at a given instant remain valid when multiple changes are allowed.     

The shuttle dispatch problem with compound Poisson arrivals: Controls at two terminals

We consider the control of an infinite capacity shuttle which transports passengers between two terminals. The passengers arrive at each terminal according to a compound Poisson process and the travel time from one terminal to the other is a random variable following an arbitrary distribution. The following control limit policy is considered: dispatch the shuttle at terminali, at the instant that the total number of passengers waiting at terminali reaches or exceeds a predetermined control limitm _i . The objective of this paper is to obtain the mean waiting time of an arbitrary passenger at each terminal for given control valuesm ₁ andm ₂. We also discuss a search procedure to obtain the optimal control values which minimize the total expected cost per unit time under a linear cost structure.