We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that o -periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a nite-bu...

Abstract: The purpose of this research is to develop algorithm calculating the traffic queue length which is main variable for effective operation at signalized intersection. For the methods to calculate the traffic queue length, there are queue theory and shock wave theory. And, the estimation of traffic queue length by existing point detection system utilizes traffic queue theory calculating ...

Mail systems comprise different components to accomplish all mail activities. On the top of these mail system functions is the message submission, delivery, and retrieval on a target host. Simple Mail Transfer Protocol (SMPT) is the mail transport protocol used to transfer mail between hosts. In SMTP session, like any protocol, two participants are involved. The first is the client that initiat...

The so-called “Israeli queue” (Boxma et al. in Stoch Model 24(4):604– 625, 2008; Perel and Yechiali in Probab Eng Inf Sci, 2013; Perel and Yechiali in Stoch Model 29(3):353–379, 2013) is a multi-queue polling-type system with a single server. Service is given in batches, where the batch sizes are unlimited and the service time of a batch does not depend on its size. After completing service, th...

K e y w o r d s B a t c h arrival, Bulk service, Hysteresis, Embedded Markov chain, Semiregenerative process, Control policy. 1. I N T R O D U C T I O N The goal of this paper is to design an optimal control policy for a batch arrival, bulk service queueing system under N-policy. In this system, customers arrive to the queueing facility in groups of random size and are served in groups of a fix...

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

Machines whose sole function is to re-order their input data are considered. Every such machine defines a set of allowable input-output pairs of permutations. These sets are studied in terms of the minimal disallowed pairs (the basis). Some allowable sets with small bases are considered including the one defined by a priority queue machine. For more complex machines defined by two or more prior...

We consider a retrial queue with a finite buffer of size N , with arrivals of ordinary units and of negative units (which cancel one ordinary unit), both assumed to be Markovian arrival processes. The service requirements are of phase type. In addition, a PH bulk service discipline is assumed. This means that the units are served in groups of size at least L, where 1 ≤ L ≤ N . If at the complet...

Five different classical bulk queueing models with variations are considered from chapter II to chapter VI. This chapter and chapter VIII are devoted for the analysis of two different retrial queueing models. Retrial queueing system is characterized by the feature that the arriving customers, who encounter the server busy, join a virtual pool called orbit. An arbitrary customer in the orbit gen...