Gautam Choudhury

Optimal design and control of queues

We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.

An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair

This paper deals with the steady state behaviour of an M/G/1 retrial queue with an additional second phase of optional service subject to breakdowns occurring randomly at any instant while serving the customers. This model generalizes both the classical M/G/1 retrial queue subject to random breakdown as well as M/G/1 queue with second optional service and server breakdowns. We carry out an extensive analysis of this model.

A two-stage batch arrival queueing system with a modified bernoulli schedule vacation under N-policy

We consider a batch arrival queueing system, where the server provides two stages of heterogeneous service with a modified Bernoulli schedule under N-policy. The server remains idle till the queue size becomes N (>= 1). As soon as the queue size becomes at least N, the server instantly starts working and provides two stages of service in succession to each customer, i.e., the first stage service followed by the second stage service. However, after the second stage service, the server may take a vacation or decide to stay in the system to provide service to the next customer, if any. We derive the queue size distribution at a random epoch as well as a departure epoch under the steady state conditions. Further, we demonstrate the existence of the stochastic decomposition property to show that the departure point queue size distribution of this model can be decomposed into the distributions of three independent random variables. We also derive some important performance measures of this model. Finally, we develop a simple procedure to obtain optimal stationary operating policy under a suitable linear cost structure.

A two phase batch arrival queueing system with a vacation time under Bernoulli schedule

We consider a batch arrival queueing system, where the server provides two phases of heterogeneous service one after the other to the arriving batches under Bernoulli schedule vacation. After completion of both phases of service the server either goes for a vacation with probability r(0=

A Batch Arrival Queue with a Second Optional Service Channel Under N-Policy

Abstract We consider an M X /G/1 queueing system with a second optional service channel under N-policy. The server remains idle until the queue size reaches or exceeds N (≥1). As soon as the queue size becomes at least N, the server immediately begins to serve the first essential service to all the waiting customers. After the completion of which, only some of them receive the second optional service. For this model, our study is basically concentrated in obtaining the queue size distribution at a random epoch as well as at a departure epoch. Further, we derive a simple procedure to obtain optimal stationary policy under a suitable linear cost structure. Moreover, we provide some important performance measures of this model with some numerical examples.

Some aspects of anM/G/1 queueing system with optional second service

This paper examines the steady state behaviour of anM/G/1 queue with a second optional service in which the server may provide two phases of heterogeneous service to incoming units. We derive the queue size distribution at stationary point of time and waiting time distribution. Moreover we derive the queue size distribution at the departure point of time as a classical generalization of the well knownPollaczek Khinchin formula. This is a generalization of the result obtained by Madan (2000).

A batch arrival retrial queueing system with two phases of service and service interruption

This paper deals with the steady-state behavior of an M^X/G/1 retrial queue with an additional second phase of optional service and service interruption where breakdowns occur randomly at any instant while the server is serving the customers. Further, the concept of delay time is also introduced in the model. This model generalizes both the classical M^X/G/1 retrial queue with service interruption as well as the M^X/G/1 queue with second optional service and service interruption. We carry out an extensive analysis of this model.

The N-policy for an unreliable server with delaying repair and two phases of service

This paper deals with an M^X/G/1 with an additional second phase of optional service and unreliable server, which consist of a breakdown period and a delay period under N-policy. While the server is working with any phase of service, it may break down at any instant and the service channel will fail for a short interval of time. Further concept of the delay time is also introduced. If no customer arrives during the breakdown period, the server becomes idle in the system until the queue size builds up to a threshold value N(>=1). As soon as the queue size becomes at least N, the server immediately begins to serve the first phase of regular service to all the waiting customers. After the completion of which, only some of them receive the second phase of the optional service. We derive the queue size distribution at a random epoch and departure epoch as well as various system performance measures. Finally we derive a simple procedure to obtain optimal stationary policy under a suitable linear cost structure.

An MX/G/1 unreliable retrial queue with two phases of service and Bernoulli admission mechanism

This paper deals with the steady state behaviour of an M^X/G/1 retrial queue with an additional second phase of optional service and unreliable server where breakdowns occur randomly at any instant while serving the customers. Further concept of Bernoulli admission mechanism is also introduced in the model. This model generalizes both the classical M^X/G/1 retrial queue subject to random breakdown and Bernoulli admission mechanism as well as M^X/G/1 queue with second optional service and unreliable server. We carry out an extensive analysis of this model.

A BULK QUORUM QUEUEING SYSTEM WITH A RANDOM SETUP TIME UNDER N-POLICY AND WITH BERNOULLI VACATION SCHEDULE

Abstract We aim in this paper at designing an optimal management policy for a bulk service queueing system with random set-up time under Bernoulli vacation schedule and N-policy. We first study the discrete time parameter and continuous time parameter stochastic processes and derive all the quantities required to build a linear cost structure. Then an algorithm is suggested to determine the optimal management policy. An illustrative example is presented to show how to implement this policy and a sensitivity analysis is conducted to determine the effect of the system parameters.