Question

The following are the sample data sets from your class project about waiting line theories:

Arrival: 4, 4, 4, 0, 4

Service time: 35, 39, 42, 69, 33

The arrival data were number of cars arrived per every 5-minute interval, and the service data were the number of seconds spent on taking the corresponding order.

The management is not satisfied with the current total amount of time (in seconds) that a customer has to spend in the overall service process and would like to see a reduction of 4% in that total time.

If the management's goal is to achieved, what would the minimum expected service rate (# cars served in a 5-min interval) has to be? Give your answer to two significant places.

Answer 1

Ans: From the data provided and that is Arrival : 4,4,4,0,4 & Service Time - 35, 39, 42, 69, 33 the expectation from management is to see a reduction of 4 % in total time and so what would be the minimum expected service rate has to be? Also the data says there is a 5 - minute interval between arrivals.

Key Takes for the answer - Number of cars are arriving at a standard rate - in batches of 4 The service sample date varries though.

So The calculation is as follows to acheive the reduction of 4 % on overall time taken by the service process.

Number of Cars	4	4	4	0	4	Average	4% Reduction	Minimum expected service time to achieve( to see 4 % reduction)
5 Min waiting time interval - conversion from minutes to Seconds ( 5*60)	300	300	300	300	300
Seconds spent on taking the corresponding order	35	39	42	69	33
Overall time taken in seconds	335	339	342	369	333	343.6	13.744	329.86
Overall time taken in Minutes	5.583333	5.65	5.7	6.15	5.55	5.726667	0.229066667	5.50

The minimum expected service rate has to be = 329.86 in seconds( arrival time + seconds spent to take corresponding order)

The minimum expected service rate has to be = 5.49 in minutes( arrival time + seconds spent to take corresponding order)

Thanks & Cheers!