© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 2 Chapter 7 TN Waiting Line Management u Waiting line characteristics u Some waiting line management tips u Examples (Models 1, 2, 3, and 4)

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 8 Suggestions for Managing Queues u Do not overlook the effects of perceptions management. u Determine the acceptable waiting time for your customers. u Install distractions that entertain and physically involve the customer. u Get customers out of line. u Only make people conscious of time if they grossly overestimate waiting times.

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 9 Suggestions for Managing Queues u Modify customer arrival behavior. u Keep resources not serving customers out of sight. u Segment customers by personality types. u Adopt a long-term perspective. u Never underestimate the power of a friendly server.

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 3 Components of the Queuing Phenomenon Customer Arrivals Servers Waiting Line Servicing System Exit

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 4 Population Sources Population Source FiniteInfinite

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 5 Service Rate Service Rate ConstantVariable

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 6 Line Structures Single Channel Multichannel Single Phase Multiphase One-person barber shop Car wash Hospital admissions Bank tellers’ windows

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 7 Degree of Patience No Way! BALK No Way! RENEG

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 10 Waiting Line Models ModelLayout Source PopulationService Pattern 1Single channelInfiniteExponential 2Single channelInfiniteConstant 3MultichannelInfiniteExponential 4Single or MultiFiniteExponential These four models share the following characteristics:  Single phase  Poisson arrival  FCFS  Unlimited queue length

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 11 Example: Model 1 Drive-up window at a fast food restaurant. Customers arrive at the rate of 25 per hour. The employee can serve one customer every two minutes. Assume Poisson arrival and exponential service rates. A) What is the average utilization of the employee? B) What is the average number of customers in line? C) What is the average number of customers in the system? D) What is the average waiting time in line? E) What is the average waiting time in the system? F) What is the probability that exactly two cars will be waiting in line?

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 12 Example: Model 1 A) What is the average utilization of the employee?

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 13 Example: Model 1 B) What is the average number of customers in line? C) What is the average number of customers in the system?

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 14 Example: Model 1 D) What is the average waiting time in line? E) What is the average waiting time in the system?

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 15 Example: Model 1 F) What is the probability that exactly two cars will be waiting in line?

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 16 Example: Model 2 An automated pizza vending machine heats and dispenses a slice of pizza in 4 minutes. Customers arrive at a rate of one every 6 minutes with the arrival rate exhibiting a Poisson distribution. Determine: A) The average number of customers in line. B) The average total waiting time in the system.

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 17 Example: Model 2 A) The average number of customers in line. B) The average total waiting time in the system.

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 18 Example: Model 3 Recall the Model 1 example: Drive-up window at a fast food restaurant. Customers arrive at the rate of 25 per hour. The employee can serve one customer every two minutes. Assume Poisson arrival and exponential service rates. If an identical window (and an identically trained server) were added, what would the effects be on the average number of cars in the system and the total time customers wait before being served?

© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 19 Example: Model 3 Average number of cars in the system Total time customers wait before being served