Chapter 7 TN Waiting Line Management u Waiting

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

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. Irwin/Mc. Graw-Hill ©The Mc. Graw-Hill Companies, Inc. , 1998 8

Suggestions for Managing Queues u Modify u Keep customer arrival behavior. 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. Irwin/Mc. Graw-Hill ©The Mc. Graw-Hill Companies, Inc. , 1998 9

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

Population Sources Population Source Finite Irwin/Mc. Graw-Hill Infinite ©The Mc. Graw-Hill Companies, Inc. , 1998 4

Service Rate Constant Irwin/Mc. Graw-Hill Variable ©The Mc. Graw-Hill Companies, Inc. , 1998 5

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

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

Waiting Line Models Model 1 Layout Single channel Source Population Infinite 2 Single channel Infinite Constant 3 Multichannel Infinite Exponential 4 Single or Multi Finite Exponential Service Pattern Exponential These four models share the following characteristics: · Single phase · Poisson arrival · FCFS · Unlimited queue length Irwin/Mc. Graw-Hill ©The Mc. Graw-Hill Companies, Inc. , 1998 10

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) B) C) D) E) F) What is the average utilization of the employee? What is the average number of customers in line? What is the average number of customers in the system? What is the average waiting time in line? What is the average waiting time in the system? What is the probability that exactly two cars will be waiting in line? Irwin/Mc. Graw-Hill ©The Mc. Graw-Hill Companies, Inc. , 1998 11

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

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

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

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

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. Irwin/Mc. Graw-Hill ©The Mc. Graw-Hill Companies, Inc. , 1998 16

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

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? Irwin/Mc. Graw-Hill ©The Mc. Graw-Hill Companies, Inc. , 1998 18

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