Optimal Policy for M^x/G/1 Queueing System with Bernoulli Feedback

Abstract

We deal with Mx/G/1 Queueing System with Bernoulli feedback under N-Policy. The probability generating function and supplementary variable technique are utilized to evaluate the steady state probability distribution of the number of units in the system. The steady state results are used to establish the explicit expressions for the average number of units in the system and the mean response time for three different series time distribution. Some of the existing results are deduced as special cases. Cost analysis is performed to design the optimal N-policy at minimum cost. In order to validate the analytical approach by taking illustration we compute numerical results.

Keywords

• M^x/G/1 Queue
• Supplementary variable
• N-policy
• Bernoulli feedback
• Response time
• Cost Analysis