P.R. Parthasarathy

Transient solution to the many-server Poisson queue: a simple approach

An elegant time-dependent solution for the number in the M/M/c queueing system is derived in a direct way.

An M / M /1 Driven Fluid Queue – Continued Fraction Approach

This paper presents complete solutions of the stationary distributions of buffer occupancy and buffer content of a fluid queue driven by an M/M/1 queue. We assume a general boundary condition when compared to the model discussed in Virtamo and Norros [Queueing Systems 16 (1994) 373–386] and Adan and Resing [Queueing Systems 22 (1996) 171–174]. We achieve the required solutions by transforming the underlying system of differential equations using Laplace transforms to a system of difference equations leading to a continued fraction. This continued fraction helps us to find complete solutions. We also obtain the buffer content distribution for this fluid model using the method of Sericola and Tuffin [Queueing Systems 31 (1999) 253–264].

Transient analysis of a queue where potential customers are discouraged by queue length.

The transient solution is obtained analytically using continued fractions for a state-dependent birth-death queue in which potential customers are discouraged by the queue length. This queueing system is then compared with the well-known infinite server queueing system which has the same steady state solution as the model under consideration, whereas their transient solutions are different. A natural measure of speed of convergence of the mean number in the system to its stationarity is also computed.

On the unutilized capacity of a production-storage system

A one-product one-machine production/inventory problem in which the machine is subject to failure, is considered. The product is stored in an inventory of finite capacity. When the machine is operable, it produces at a rate @a greater than the demand rate @b, until the inventory becomes full and thereafter it produces at the demand rate. This stepping down of the rate of production results in the under-utilisation of the machine. The under-utilisation of the machine and the demand not met are analysed; special cases are considered. Cost analysis is also indicated.

Cost Analysis for 2-Unit Systems

For a 2-unit system with general repair and failure time distributions, the net profit has been studied as the difference between functions of the uptime and downtime. The mean number of products manufactured is also given.

Transient Solution of an M/M/1 Queue with Balking

An infinite capacityM/M/1 queue with balking is discussed. Defining the generating function in an unusual and direct way, the time-dependent solution for the system size is obtained elegantly.

Time-dependent analysis of a single-server retrial queue with state-dependent rates

For a single-server retrial queue with state-dependent exponential interarrival, service and inter-retrial times, we study the time-dependent system size probabilities by employing continued fractions and numerical illustrations are presented.

Exact transient solution of a state-dependent birth-death process

A power series expression in closed form for the transient probabilities of a state-dependent birth-death process is presented with suitable illustrations.

Fluid queues driven by an M/M/1/N queue

In this paper, we consider fluid queue models with infinite buffer capacity which receives and releases fluid at variable rates in such a way that the net input rate of fluid into the buffer (which is negative when fluid is flowing out of the buffer) is uniquely determined by the number of customers in an M/M/1/N queue model (that is, the fluid queue is driven by this Markovian queue) with constant arrival and service rates. We use some interesting identities of tridiagonal determinants to find analytically the eigenvalues of the underlying tridiagonal matrix and hence the distribution function of the buffer occupancy. For specific cases, we verify the results available in the literature.

Transient solution of a multiserver Poisson queue with N-policy

We consider an M/M/c queueing system, where the server idles until a fixed number N of customers accumulates in a queue and following the arrival of the N-th customer, the server serves exhaustively the queue. We obtain the exact transient solution for the state probabilities of this N-policy queue by a direct approach. Further we obtain the time-dependent mean, variance of this system and its busy period distribution.