Question

I want you to be able to witness first-hand the effects of utilization and variability on queueing performance by drawing a throughput-delay curve based on the following information:A grocery store has 1 checkout counter where a clerk processes customers at an average rate of 2 per minute. Customers arrive at an average rate of 1 per minute. Assume inter-arrivals and processing times are exponentially distributed. Use excel to draw graphs.

a) Everything else staying the same, chart the average flow time as customer arrival rate increases from 1 to 1.9 per minute in increments of 0.1. (10 points)

b) The clerk gets tired as the day winds on. Chart the average flow time when arrival rate stays fixed at 1 per minute but the average
processing time goes from 0.5 minutes to 0.9 minutes in increments of 0.05 minutes. (10 points)

c) Assume an arrival rate of 1.9 customers per minute. Everything else staying the same (processing rate is 2 per minute per clerk), chart what happens when you increase the number of clerks (checkout counters) in increments of 1 up to 5. Assume that all customers queue up in a single line. (10 points)

d) Assume an arrival rate of 1.9 customers per minute. Everything else staying the same (processing rate is 2 per minute per clerk), chart what happens when you increase the number of clerks (checkout counters) in increments of 1 up to 5. Assume that all customers queue up in separate lines. (10 points)

Answer 1

Solution:

a)

Average flow time or time in system, W = 1/(-), where is the processing or service rate and is the customer arrival rate

Ceate a table using the above formula and based on the table, create chart as follows:

Chart is created using data in column A and C only

EXCEL FORMULAS:

b)

Create table and chart as follows:

Chart is create using data in column D and D only

EXCEL FORMULAS:

c)

Using multiple servers, it becomes a M/M/s queue model

Use following spreadsheet to compute the Average flow time

EXCEL FORMULAS:

d)

In the spreadsheet model, change the value in cell D6 from 1 to 5 for different number of clerks and note the down the value of W for each number of clerks. Use those values to create a table and chart as shown below

Note that there are no formulas in the above table