J Syst Sci Syst Eng (Sep 2010) 19(3): 367-384 ISSN: 1004-3756 (Paper) 1861-9576 (Online) DOI: 10.1007/s11518-010-5138-6 CN11-2983/N © Systems Engineering Society of China & Springer-Verlag Berlin Heidelberg 2010 ANALYSIS OF A DISCRETE-TIME GI/GEO/1/N QUEUE WITH MULTIPLE WORKING VACATIONS Veena GOSWAMI 1 G.B. MUND 2 1 School of Computer Application, KIIT University, Bhubaneswar 751024, India veena_goswami@yahoo.com () 2 School of Computer Engineering, KIIT University, Bhubaneswar 751024, India mundgb@yahoo.com Abstract This paper analyzes a finite-buffer renewal input single server discrete-time queueing system with multiple working vacations. The server works at a different rate rather than completely stopping working during the multiple working vacations. The service times during a service period, service time during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer’s observation epochs. The analysis of actual waiting-time distribution and some performance measures are carried out. We present some numerical results and discuss special cases of the model. Keywords: Discrete-time, finite-buffer, working vacations, supplementary variable, waiting-time 1. Introduction Queueing systems with server vacations have been studied extensively due to their wide applications in several areas including computer and communication systems, manufacturing and production systems. More details have been reported in Doshi (1986), Takagi (1991) and Tian & Zhang (2006). In the study of vacation models, the server is generally assumed to stop service completely during vacation period. However, there are numerous situations where the server remains active during the vacation period and serve the customers at a different service rate. At the end of a vacation if the queue is nonempty a service period begins and the server serves the system with its usual service rate; otherwise the server takes another vacation. Servi & Finn (2002) introduced the concept of such multiple working vacations. They studied an M/M/1 queue with multiple working vacations (M/M/1/WV). Wu & Takagi (2006) generalized Servi & Finn’s M/M/1/WV queue to an M/G/1/WV queue. Baba (2005) extended this study to a renewal input GI/M/1 queue with working vacations and derived the steady state system length distributions at an arrival and arbitrary epochs. The single/multiple vacation time queues with renewal input have been studied extensively by Chae et al. (2007), Tian et al. (1989), Chatterjee