ABC Salon is a hair salon with two stylists, Mary and Mike. Each stylist can ser
ID: 408925 • Letter: A
Question
ABC Salon is a hair salon with two stylists, Mary and Mike. Each stylist can serve four customers per hour, on average, exponentially distributed. Six customers, on average, arrive at the salon every hour.
A. If all arriving customers wait in a common line for the next available stylist, how long would a customer wait in line, on average, before being served?
B. Suppose that 50% of the arriving customers want to be served only by Mary, and the other 50% want to be served only by Mike. How long would a customer wait in line, on average, before being served by Mary? By Mike? What is the average time a customer spends waiting in line?
C. Do you observe a difference in the answers to parts (a) and (b)? If so, explain.
Explanation / Answer
Arrival rate is 6 (six) per hour and there are two servers (Mary and Mike). Each server can serve 4(four) per hour.
Solution to part A is as follows:
For B Assumption is that 50% of customers are for Mary and 50% for Mike, therefore we may have two separate queues and the arrival rate may be considered as (6/2) 3 per hour for each one with service rate same 4 per hour.
Solution is as follows:
As apparent from above in case of B average time a customer spends waiting in line has increased
Parameter Value Parameter Value Minutes Seconds M/M/s Average server utilization 0.75 Arrival rate(lambda) 6 Average number in the queue(Lq) 1.9286 Service rate(mu) 4 Average number in the system(Ls) 3.4286 Number of servers 2 Average time in the queue(Wq) 0.3214 19.2857 1,157.14 Average time in the system(Ws) 0.5714 34.2857 2,057.14