OM 17 Queuing

Question 1

Goal of Witing Line Management

Answer 1

minimize total cost = customer waiting cost + capacity costs

Question 2

Waiting Line Characteristics (4)

Answer 2

1. Population Source
2. Number of Servers (Channels)
3. Arrival and Service Patterns
4. Queue discipline

Question 3

Waiting Line Characteristics: Population Source

Answer 3

Infinite source: Customer arrivals are unrestricted and # of potential customers greatly exceed system capacity (Grocery store)
Finite Source

Question 4

Waiting Line Characteristics: Number of Servers/ Channels

Answer 4

single or multichannel: surgical team

Question 5

Waiting Line Characteristics: Arrival and Service Patterns

Answer 5

Arrival Rate: Poisson distribution
Interarrival and Service Time: Negative exponential distribution
- The higher frequency of services, the shorter the service time (bad accident, long time)

Question 6

Waiting Line Characteristics: Queue Discipline

Answer 6

= order in which customers are processed

- first come first serve, appointment

Question 7

Waiting Line Metrics

Answer 7

1. avg # of customers waiting
2. Avg wait time
3. System Utilization (extent to which servers are busy)
4. Implied cost of a given level of capacity and wait time
5. Probability that arrival will have to wait for service

Question 8

Four Basic Infinite Source Models

Answer 8

1. Single Server, Exponential Service Time
2. Single Server, Constant Service Time
3. Multiple Servers Exponential Service Tiem
4. Multiple Priority service, exponential service times

Question 9

Little’s Law

Answer 9

For a stable system, the average number of customers in line or in the system is equal to the average customer arrival rate multiplied by the average time in the line or the system