Cost and Profit Analysis of a Queueing System with K Phases Heterogeneous Services and Vacation

In this paper, cost and profit analysis of a queueing system with k phases heterogeneous services and vacation is studied. The service times and vacation times have general distribution. It is assumed that the time between two successive arrivals has exponential distribution. Also we assume that service times, vacation time and inter arrival time are independent. After completion of k phases of services, for same reasons, the server takes vacation with given probability and after completion of this period, the server waits idle for a client. Considering the importance of economic factors and optimization in queueing systems, in this model we define expected total cost for finding the optimum service rate. Also with expected total revenue, the total profit of system in analyzed in comparison to total cost of system. Finally in a case study, with special distributions and numerical methods the validity of system is studied with respect to its parameters.