Question

Waiting lines Customers walk in at random to a deli. The interarrival times are exponentially distributed with an average of 5 minutes. The deli prepares one order at a time. The order preparation times are exponentially distributed with an average of 3 minutes. 13. What kind of waiting line model is appropriate for the deli? 14. What is the utilization? 15. What is the total amount of time a customer would expect to spend at the deli (from walking in until walking out with a sandwich)? if the deli conducted a process improvement exercise to standardize the sandwich making process (i.e., eliminate as much process variability as possible), would the answer to #15 b larger, smaller, or the same? Why? 16. I

Answer 1

(a) M/M/1 queuing model is the most appropriate for this type of waiting line model.

(b)

Lambda = Arrival rate = 60/5 =12 per hour

Mu = Service rate =60/3 =20 per hour

Utilization = arrival rate / service rate = 12/20 =0.6 = 60%

(c) Total time in the system-

Ws = 1/mu-lambda = 1/ 20-12 = 1/8 hours = 7.5 minutes

(d) If a process improvement exercise is conducted, the waiting time in queue as well as in system is expected to  reduce.