M/M/S Queueing Theory Model to Solve Waiting Line and to Minimize Estimated Total Cost

The model describe in this paper is the multiple-server queuing model with Poisson Arrival and Exponential Service Times (M/M/S). We find the total minimum expected cost. Total expected costs are studied, total costs is the sum of the cost of providing service plus the cost of waiting time. Queuing is the common activity of customers or people to avail the desired service, which could be processed or distributed one at a time. Waiting lines and service systems are important parts of the business world. In this paper we describe several common queuing situations and present mathematical models for analyzing waiting lines following certain assumptions. Those assumptions are, arrivals come from an infinite or very large population, arrivals are Poisson distributed, arrivals are treated on a FIFO basis and do not balk or renege, service times follow the negative exponential distribution or are constant, and the average service rate is faster than the average arrival rate.