Question

a. The Arctic Flyers minor league hockey team has one box office clerk. On average, each customer that comes to see a game can be sold a ticket at a rate of 8 per minute. For regular games, customers arrive at a rate of 5 per minute. Assume arrivals follow the Poisson distribution, and service times follow the exponential distribution What is the average number of customers waiting in line? What is the average time a customer spends in the waiting line (minute)? What is the average number of customers in the system? d. What is a customer's average time in the system (minute)? b.

Answer 1

1. Average number of customer waiting in the line= (Arrival Rate)^2/((Service rate*(Service Rate-Arrival Rate))

Average number of customer waiting in the line=(5)^2/(8*(8-5))

Average number of customer waiting in the line =1.042

2. Average time a customer spends in the waiting line= Average number of customer waiting in the line/ Arrival Rate

Average time a customer spends in the waiting line=1.042/5

Average time a customer spends in the waiting line =0.2084 Minutes

C)

Average number of customers in the system= Average number of customer waiting in the line+(Arrival Rate/ Service rate)

Average number of customers in the system=1.042+(5/8)=1.667

D)

Customer’s average time in the system= Average time a customer spends in the waiting line+(1/service rate)

Customer’s average time in the system = 0.2084+ (1/8)

Customer’s average time in the system=0.3334 Minutes