Question

1. A simple queueing system has an arrival rate of 6 per hour and a service rate of 10 per hour. For this system the average time in line has been estimated to be 20 minutes. Using Little’s Law estimate the following:
   1. Average time in the queueing system
   2. Average number of customers in the queueing system
   3. Average number of customers in the queue
   4. Average number of customers in service.

Answer 1

arrivals/time period =			λ=	6
served/time period=			μ=	10.00

a)

Average time in the queueing system:

average time spend in system W                   =

1/(μ-λ)=

0.25 Hours

b)

average number of customers in system L =

λ/(μ-λ)=

1.5

c)

average number of customers in queue Lq =

λ2/(μ(μ-λ))=

0.90

d)

Average number of customers in service =1.5-0.9 =0.6