고객(顧客)이 임의수(任意數)의 Server 를 원하는 M/M/s system 의 개산법(槪算法)

An approximation of the M/M/s system where customers demand random number of servers

In the case of numerical implementation, the exact solution method for the M/M/s system where customers demand multiple server use [2] reveals limitations, if a system has large number of servers or types of customers. This is due to the huge matrices involved in the course of the calculations. This paper offers an approximation scheme for such cases. Capitalizing the characteristics of the service rate curve of the system, this method approximates the service rate as a piecewise linear function. With the service rates obtained from the linear function for each number of customers n (n=0. 1. 2,$\cdots$), ${\mu}(n)$, steady-state probabilities and measures of performance are found treating this system as an ordinary M/M/s system. This scheme performs well when the traffic intensity of a system is below about 0.8. Some numerical examples are presented.