Maximum Entropy Analysis of M^X/G/1 Retrial Queue with k-Phases of Heterogeneous Service and Impatient Calls Under Different Vacation Policies

SYNOPTIC ABSTRACT

This work studies the steady state behavior of an M^x/G/1 retrial queue with k-phases of heterogeneous service under different vacation policies. If the server is busy or on vacation, an arriving batch of calls either becomes impatient and balks (leaves) the system with some probability or enters in the virtual pool of blocked calls called “orbit.” The server provides service in k-phases to all the calls. After completing the kth phase of essential service of a call, the server has an option to go for lth (l = 1,2,…,M) type of vacation with probability η_l (l = 1,2,…,M) or to continue to serve the next call (if any) with probability η₀where . The explicit expressions for the expected number of calls and expected waiting time of the calls in the retrial group are obtained using supplementary variable and generating function techniques. The maximum entropy principle is also employed to derive various system performance characteristics. A comparative analysis between the approximate results and the established exact results for waiting time distribution have been presented. The sensitivity analysis is carried out to demonstrate the tractability of the analytical results.

Key Words and Phrases::

• bulk arrival
• retrial queue
• supplementary variable
• generating function
• maximum entropy principle.