Question

Suppose a queueing system fitting the M/M/1 model has W = 120 minutes and L = 8 customers. Use these facts (and the formula for W) to find λ and μ and explain what are λ and μ.

Answer 1

solution:

let a =

and let

so

in M/M/1 model:

W denotes the average time a customer spen in the system

.........................eq 1

L denotes the average number of customer in the system

and

  

multiplying by 15 both sides

.......................eq 2

from eq 1 and 2 we get

putting the value of in eq 1 we get

here means average number of items or customer served per time period

means average number of arrival of customer per time period