Performance Analysis of Working Vacation Queueing Models in Communication Systems

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This thesis studies, both analytically and through numerical experiments, the performance of queueing models with a `working vacation' policy arising naturally in communication systems, especially in wavelength division multiplexing (WDM) networks. In a queueing system with this vacation policy, the server switches between vacation and non-vacation periods. Unlike in a classical vacation framework, this system serves customers even during vacation periods but at a lower service rate. We study some working vacation queueing models incorporating diDerent features of system characteristics with a view to assisting optimization and guiding the design of new generation systems. First, we consider a single-server queueing model with working vacations and corre- lated arrivals as network traDc is seldom similar and this often leads to system congestion and packet loss. The model is studied in discrete-time scale by constructing a quasi-birth- death (QBD) process. Since the matrix-geometric method gives an eDcient way to solve homogeneous QBDs, we use this method to analyze and study the performance of the correlated model. The analogous continuous-time model is also outlined. Next, we con- sider a Dnite-buDer model with this working vacation policy and correlated arrivals to lay the emphasis on the role of correlation in arrivals on customer loss probabilities. A multi- server model is presented next, where the servers obey asynchronous multiple working vacation policy and the formulated non-homogeneous QBD process is analyzed using the Dnite truncation method of approximation. A working vacation model with diDerent priority classes of customers is studied as priority based traDc can enhance network eDciency and ensure quality of service (QoS). Explicit expressions for system performance measures are obtained and also comparisons are made for diDerent classes of customers. Another important model considered is with retrial or repeated attempts of customers. This model, mostly seen in mobile networks, is analyzed to obtain closed-form solutions. Finally, a queue with impatient customers is studied with two types of working vacation policies, multiple and single working vacation policy, and comparisons are made to determine the most effective policy....
Supervisor: N Selvaraju