Category: Customer Relationship Management Copyright © 2018, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 1570 DOI: 10.4018/978-1-5225-2255-3.ch136 Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy INTRODUCTION Waiting in line is an experience that everyone practices, almost, on a daily basis. The waiting takes different forms and settings. Nowadays, the competition of customer satisfaction and low cost becomes very intense to the point that any customer that waits too long in line is potentially a lost customer to another compactor that provides better service or better waiting environment. Waiting lines are basic in structure to the ex- ternal (customer-facing) and the internal business processes. Queueing structures generally include staffing, scheduling and inventory levels. For this reason, businesses often utilize queuing theory as a competitive advantage. Although queuing is undesired for anyone, it is the cornerstone of efficiency and organization for many companies. The idea is simple: At any given moment, there can be more people or cases needing service, help or attention than an organization can handle. Queues help workers and managers track, prioritize and ensure the delivery of services and transactions. The theory of waiting lines provides insight and identifies management options for improving customer service. A wide variety of queueing models have been developed and successfully exploited for very complex service situations. This chapter describes one such queueing model. For a comprehensive classification of various control policies applied in queueing systems, see the survey by Tadj and Choudhury (2005). The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. It is assumed that at the end of a given service, the server may either take a vacation or start serving the next customer. When the queue is empty, the server again takes vacations and scans the queue periodically, every T units of time, to check if some customers have arrived while he was away. The third assumption is that the actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. BACKGROUND The unreliability of the server is one of the main features of the queueing system studied in this chapter. Queueing systems prone to failure are commonly encountered in the real world. The server breakdown was first analyzed by White and Christie (1958). Since then, queueing systems with unreliable servers have been extensively studied by many researchers; see Tadj et al. (2012) for a comprehensive survey on the subject. The next feature of the system of interest in this chapter is the Bernoulli vacation schedule. The classical vacation scheme with Bernoulli service discipline was introduced and developed by Keilson and Servi (1986). Various aspects of Bernoulli vacation models have been discussed Khalid Alnowibet King Saud University, Saudi Arabia Lotfi Tadj Fairleigh Dickinson University, Canada