WAITING LINES AND SIMULATION

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Presentation transcript:

WAITING LINES AND SIMULATION PART SEVEN WAITING LINES AND SIMULATION Chapter Nineteen Waiting Lines Chapter 19 Supplement Simulation

Chapter 19 Waiting Lines

Goal of queuing analysis is to minimize the sum of two costs Waiting Lines Queuing theory: Mathematical approach to the analysis of waiting lines. Goal of queuing analysis is to minimize the sum of two costs Customer waiting costs Service capacity costs

Implications of Waiting Lines Cost to provide waiting space Loss of business Customers leaving Customers refusing to wait Loss of goodwill Reduction in customer satisfaction Congestion may disrupt other business operations

Queuing Analysis Figure 19-1 Cost Service capacity Optimum Total cost Customer waiting cost Capacity cost = + Total cost Cost Cost of service capacity Cost of customers waiting Service capacity Optimum

System Characteristics Population Source Infinite source: customer arrivals are unrestricted Finite source: number of potential customers is limited Number of observers (channels) Arrival and service patterns Queue discipline (order of service)

Elements of Queuing System Arrivals Service Waiting line Exit Processing order System

Queuing Systems Multiple channel Multiple phase

Poisson Distribution Figure 19-4

System Performance Measured by: Average number of customers waiting Average time customers wait System utilization Implied cost Probability that an arrival will have to wait

Waiting Time vs Utilization Figure 19-6 System Utilization Average number on time waiting in line 100%

Queuing Models: Infinite-Source Single channel, exponential service time Single channel, constant service time Multiple channel, exponential service time Multiple priority service, exponential service time

Queuing Models Single channel, exponential service time Single channel, constant service time Multiple channel, exponential service time Multiple priority service

Priority Model Arrivals Service Waiting line Exit Processing order System 1 2 3 Arrivals are assigned a priority as they arrive

Finite-Source Formulas Table 19-6 Average number being served Service factor Average number waiting Average waiting time Average number running Number in population

Finite-Source Queuing Not waiting or being served Waiting Being served J L H U W T