Improving efficiency of the queueing system with two types of customers by service decomposition

The economic improvements of a queueing system with two types of customers achieved by service decomposition are examined. The service process for a Type 2 customer can be split into two phases: a basic service and an additional service. The basic service rate is equal to that of the Type 1 customer. Additional services can be viewed as orders stored in inventory and processed when the server is idle. Once a new customer arrives during idle time, the server will provide a basic service to the customer upon his/her arrival. That is, customers have preemptive priority for orders stored in inventory. We obtain a two-dimensional unbounded Markov process and apply the multivariate generating function to derive the stationary probability of the proposed model as well as some performance measures. The condition under which performing service decomposition can improve economic efficiency is also obtained. Both the optimal inventory capacity and the minimum system cost are obtained numerically. Numerical experiments demonstrate the impact of optimal inventory setting on economic improvement efficiency. Finally, simulation experiments prove the correctness of our theoretical analysis.