Answer to Question #222684 in Management for joe

Question

A and C mall is a busy centre for residents in East Legon and its sourrounding community. Assume that 2 customers arrive every 12 minutes and 3 customers are served every 15 minutes and that currently, there is only one cashier. 

 

(i) Determine the average waiting time in minutes before service begins. AN(1mark)

 

(ii). Advice the management the proportion of the time that a customer has to wait.  AN(4marks)

 

 

Answer 1

A. Existing Scenario:

Excel Formulation

A C D E 1 B Existing Scenario Average time for customer arrival average service time 2 2 B 4 =12/2 =15/3 3 4 2 5 6 Customer A

Eating Scenario

Average time for customer arrival = 6

average service time =5

Customer Arrival Rate( λ ) = 0.17

Service rate(μ) = 0.2

Server Utilization P = 8.83

Number in the Queue Lq = 4.17

Number in the System Lr = 5.00

Waiting time In Queue Wq = 25

Waitin time in System Ws = 30

Part i:

Before the service starts, the average wait time in the system is 30 minutes.

Part ii:

The average waiting time in queue is 25 min, customer has to wait 25 min before its turn come for service. The proportion with total waiting time in the system is 25/30 min i.e. 5/6