Statistical Methodology 3 (2006) 174–185 www.elsevier.com/locate/stamet A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy ✩ Gautam Choudhury ∗ , Madhuchanda Paul Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragoan, Guwahati – 781035, Assam, India Received 30 December 2003; received in revised form 6 June 2005; accepted 16 September 2005 Abstract This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0 ≤ p ≤ 1) or may continue to serve the next unit, if any, with probability q (= 1 - p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues. c  2005 Elsevier B.V. All rights reserved. MSC: primary 60K25; secondary 90B22, 68M20 Keywords: M/ G/1 queue; Heterogeneous service; First phase of service; Second phase of service; Bernoulli schedule vacation; Multiple vacation policy; Statistical analysis 1. Introduction Recently Madan [15,16] studied the M/ G/1 queueing system with two phases of heterogeneous service viz. first phase of service (FPS) followed by a second phase of service (SPS) under a Bernoulli vacation schedule. In fact the Bernoulli vacation model was first studied by Keilson and Servi [10], where they introduced the concept of modified service time. ✩ This work is supported by Department of Atomic Energy, Govt of India, NBHM. Project No. 48/2/2001/R&DII/1211. ∗ Corresponding author. Tel.: +91 031 2513123; fax: +91 0361 2222660. E-mail addresses: choudhuryg@yahoo.com (G. Choudhury), to madhu paul@yahoo.com (M. Paul). 1572-3127/$ - see front matter c  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.stamet.2005.09.003