Question

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 9 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 15 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of W_q for each alternative.

A. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 19 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations.

Wq=

B. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 15 customers per hour for each server. Note: Use P₀ values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations.

Wq=

Answer 1

Ans: (a) Gien arrival Tate Cas is customeas Ifout) - searice rate = CM2 = 19 customer /hour Wq = = - 10.19736] nons M(4-1) 19619-15) (b) service dule = 15 customeo haur 7-15 Customeos hour. at 2-sedves operation, K=2 - wq = La tere. Lq = (n/)* + DAM (Hills) 4 15 415 (K-1)! (KN-2)2 (2-) (@(15)-1s5j6 LI=1 Now, wq = b 2 = 1 / 2 = 0.5 hours i (9) Wq auf server Operator cwq = 0.19736 honas (h) at two-server operator = wq = 0.5 hours