Performance Analysis of a Renewal Input Bulk Service Queue with Accessible and Non-Accessible Batches

Abstract

In this paper, we consider a single-server infinite-(finite-) buffer bulk-service queues. The interarrival and service times are respectively, arbitrarily and exponentially distributed. The customers are served by a single server in accessible or non-accessible batches of maximum size ‘b’ with a minimum threshold value ‘a’. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state queue length distributions at prearrival and arbitrary epochs. Finally, some numerical results have been presented.

Key Words:

• Accessible batch
• bulk-service
• non-accessible batch
• supplementary variable

Additional information

Notes on contributors

V. Goswami

V. Goswami is currently a Professor in the School of Computer Application, KIIT University, Bhubaneswar, India. She received her Ph.D. degree from Sambalpur University, India, in the year 1994 and then worked as post doctoral fellow at Indian Institute of Technology, Kharagpur for two years. Her research interests include continuous-and discrete-time queues. She has published research articles in INFORMS Journal on Computing, Computers and Operations Research, RAIRO Operations Research, Computers and Mathematics with Applications, Computers and Industrial Engineering, Applied Mathematical Modelling, Applied Mathematics and Computation, etc.

P. Vijaya Laxmi

P. Vijaya Laxmi is an Assistant Professor in the Department of Applied Mathematics, Andhra University, Visakhapatnam, India. She did M.Sc and Ph.D. from Indian Institute of Technology, Kharagpur, India in 1995 and 2003, respectively. Her main areas of research interest are continuous and discrete-time queueing models and their applications. She has publications in various Journals like Operations Research Letters, Queueing Systems, Applied Mathematical Modelling, etc.