NUMERICAL STUDY OF OPTIMAL BUFFER SIZE AND VACATION LENGTH IN M/G/1/K QUEUES WITH MULTIPLE VACATIONS

Abstract

Nowadays, due to the advent of clouding computing, buffer size can be readily extended in a couple of minutes for computing servers, where the buffer size should not be considered as given when optimizing the system performance. In this context, we explore optimal combinations for the buffer size and the length of vacation time in M/G/1/K queues with multiple vacations numerically. We consider the cases of deterministic and exponentially distributed vacation and service times. In order to do this, we also formulate an optimal problem and define cost factors: the customer loss cost, the buffer holding cost, and the server operating cost. We present some numerical examples to investigate the impact of the system parameters such as the buffer size, the length of the vacation time, and the distribution of the service time, to performance measures and the total cost. We also investigate optimal combinations for the buffer size and the vacation length for various values of the cost factors.