1 Ardavan Asef-Vaziri Sep-09 Operations Management: Waiting Lines3 Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution. The service time is 5 min per customer and has Exponential distribution. On average how many customers are in the waiting line. How long a customer stays in the line. How long a customer stays in the processor (with the server)? On average how many customers are with the server. On average how many customers are in the system ? On average how long a customer stay in the system ? Problem 1. M/M/1 Performance Evaluation

1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3 Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution

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3 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3 A local GAP store on average has 10 customers per hour for the checkout line. The inter-arrival time follows the exponential distribution. The store has two cashiers. The service time for checkout follows a normal distribution with mean equal to 5 minutes and a standard deviation of 1 minute. On average how many customers are in the waiting line. How long a customer stays in the line. How long a customer stays in the processors (with the servers)? On average how many customers are with the servers. On average how many customers are in the system ? On average how long a customer stay in the system ? Problem 3: M/M/c

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1Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3

Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution. The service time is 5 min per customer and has Exponential distribution. On average how many customers are in the waiting line. How long a customer stays in the line. How long a customer stays in the processor (with the

server)? On average how many customers are with the server. On average how many customers are in the system ? On average how long a customer stay in the system ?

Problem 1. M/M/1 Performance Evaluation

Page 2: 1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3 Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution

2Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3

Problem 2. M/M/1 Performance EvaluationWhat if the arrival rate is 11 per hour?

Page 3: 1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3 Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution

3Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3

A local GAP store on average has 10 customers per hour for the checkout line. The inter-arrival time follows the exponential distribution. The store has two cashiers. The service time for checkout follows a normal distribution with mean equal to 5 minutes and a standard deviation of 1 minute.

On average how many customers are in the waiting line. How long a customer stays in the line. How long a customer stays in the processors (with the

servers)? On average how many customers are with the servers. On average how many customers are in the system ? On average how long a customer stay in the system ?

Problem 3: M/M/c

Page 4: 1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3 Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution

4Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3

A call center has 11 operators. The arrival rate of calls is 200 calls per hour. Each of the operators can serve 20 customers per hour. Assume interarrival time and processing time follow Poisson and Exponential, respectively. What is the average waiting time (time before a customer’s call is answered)?

Problem 4