Question

A new full-service, attendant-staffed fuel and car service station on Interstate 95 will service only northbound cars. The manager estimates that customers will arrive every 4 minutes and will require 6 minutes to be served at the pump. How many pumps should be installed if the manager desires a utilization factor of 0.75? What percent of the time will the pumps be idle? Assume that the coefficients of variation of both the inter-arrival times and the service times are equal to 1.

Answer 1

customer arrival rate = 4 min, = 60/4 = 15 per hour

customer service rate = 6 min, = 60/6 = 10 per hour

utilization factor =custmoer arrival rate/(customer service rate * no.of systems)= 0.75

=> 0.75 = 15/(10 * no.of pumps)

=>no.of pumps = 15/ ( 10 * 0.75) = 15/7.5 = 2

Percentage of time pumps are idles means the time when there are zero customers, so lets find out probability of zero customers in the system.

Po =

=> Po = [ (0.75)^0/0! + (0.75)^1/1! + ((0.75)^2/2! X (1/(1-0.75))) ]^-1 = 0.34786

Therefore percent of time pumps are idle = 0.34786*100 = 34.786