Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations

We examine an M/D/2 queue with Bernoulli schedules and a single vacation policy. We have assumed Poisson arrivals waiting in a single queue and two parallel servers who provide identical deterministic service to customers on first-come, first-served basis. We consider two models; in one we assume that after completion of a service both servers can take a vacation while in the other we assume that only one may take a vacation. The vacation periods in both models are assumed to be exponential. We obtain steady state probability generating functions of system size for various states of the servers

Transient behavior of M[x]/G/1 Retrial Queueing Model with Non Persistent Customers, Random break down, Delaying Repair and Bernoulli Vacation

In this paper we consider a single server batch arrival non-Markovian retrial queueing model with non persistent customers. In accordance with Poisson process, customers arrive in batches with arrival rate  and are served one by one with first come first served basis. The server is being considered as unreliable that it may encounter break down at any time. In order to resume its service the server has to be sent for repair, but the repair does not start immediately so that there is a waiting time before the repair process. The customer, who finds the server busy upon arrival, can either join the orbit with probability p or he/she can leave the system with probability 1-p. More details can be found in the full paper. Key words: Batch size, break down, delay time, transient solution, steady solution,  reliability indices

Transient analysis of a two-heterogeneous servers queue with impatient behavior

AbstractRecently, [1] have obtained the transient solution of multi-server queue with balking and reneging. In this paper, a similar technique is used to drive a new elegant explicit solution for a two heterogeneous servers queue with impatient behavior. In addition, steady-state probabilities of the system size are studied and some important performance measures are discussed for the considered system

Study on the Departure Process of Discrete-Time Geo

This paper presents an analysis of the departure process of a discrete-time Geo/G/1 queue with randomized vacations. By using probability decomposition techniques and renewal process, the expression of expected number of departures during time interval (0+,n+] is derived. The relation among departure process, server state process, and service renewal process is obtained. The relation displays the decomposition characteristic of the departure process. Furthermore, the approximate expansion of the expected number of departures is gained. Since the departure process also often corresponds to an arrival process for a downstream queue in queueing network, it is hoped that the results obtained in this paper may provide useful information for queueing network

M (X)/G/1 WITH TWO PHASE OF HETEROGENEOUS SERVICE UNDER DIFFERENT VACATION POLICY , RESTRICTED ADMISSIBILITY AND SET UP

In this paper, we consider a batch arrival queueing system with two stage of heterogeneous service with different vacation policy subject to Restricted admissibility  and set up time is considered. Customers arrive in batches according to compound Poisson process with rate  and are served one by one in FIFO basis. After first-stage service the server must provide the second stage service. The service times of two phase of heterogenous services follow arbitrary (general) distribution with different vacation policies. Before providing service to a new customer or a batch of customers that joins the system in the renewed busy period, the server enters into a setup time process such that setup time follows exponential distribution. In addition we assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times . The probability generating function for the number of customers in the queue is found using the supplementary variable technique. The mean number of customers in the queue and the system are also found

Waiting times in a two-queue model with exhaustive and Bernoulli service

Network Analysis;operations research