Performance evaluation of a single queue capable of handling two like jobs as a single entity

In this paper, we model an open queuing network and analyze performance measures with and without feedback as two individual cases. The model comprises a single queue with a dedicated processor capable of handling two like jobs as a single job. Two different job arrivals with different processing times are considered with an internal timer. Performance measures such as average queue length, average response time, average waiting time of the jobs are computed and plotted. The joint density function for the inter arrival time and arrival rate are derived. The probability mass function has been derived for all possible cases that may arise in a duration (0, t], considering n job arrivals during that period of time and an integer programming problem is formulated to obtain optimal sequence patterns which would maximize the efficiency of the model.