Title: Queueing model with non-homogeneous bulk arrivals having state-dependent service rates

Authors: A.V.S. Suhasini; K. Srinivasa Rao; P. Rajasekhara Reddy

Addresses: Department of Statistics, Sri Venkateswara University, Tirupati, India ' Department of Statistics, Andhra University, Visakhapatnam, India ' Department of Statistics, Sri Venkateswara University, Tirupati, India

Abstract: This paper considers a single-server queueing model with non-homogeneous bulk arrivals and state-dependent service rates. The bulk arrival queueing model is important in developing optimal operating policies for queueing in transportation systems and communication systems. Arrivals are assumed to be characterised by a non-homogeneous compound Poisson process, and the service rate depends on the content of the buffer connecting to the service station. Using difference-differential equations and a probability generating function, the system's behaviour is analysed. Explicit expressions are derived for performance measures including average number of customers in the queue and probability of queue emptiness, etc. Sensitivity analysis of the model revealed that assuming non-homogeneous arrival significantly influences the system performance measures. The state-dependent service rate strategy can control queue congestion and mean delay in transmission. This model is effective in evaluating the performance of time-dependent communication systems.

Keywords: non-homogeneous Poisson arrivals; bulk arrivals; performance evaluation; compound Poisson process; transient analysis; queueing models; state-dependent service rates; modelling.

DOI: 10.1504/IJOR.2014.064023

International Journal of Operational Research, 2014 Vol.21 No.1, pp.84 - 99

Received: 17 Oct 2012
Accepted: 06 Feb 2013
Published online: 30 Aug 2014 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article