Performance and cost analysis of a finite capacity queue with two heterogeneous servers under F-policy

All previous works on F-policy queues with multiple servers have focused on multiple homogeneous servers. This paper presents an analytical analysis on the F-policy M/M/2/K queue with heterogeneous servers. We obtained the steady-state distribution of the number of customers in the system and developed a variety of performance measures. The expected cost function was constructed to determine the optimal threshold value and optimal service rates with the objective of minimising the expected cost per unit time. To this end, we developed an algorithm based on the quasi-Newton method to solve the problem of cost minimisation. Finally, sensitivity analysis was conducted using numerical examples.