L14_ThroughputLoss_B4 - Slide 1 Lecture 14 Throughput...

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Unformatted text preview: Slide 1 Lecture 14 Throughput Losses Slide 2 Consequences of Variability Waiting time Waiting for service (in the queue/buffer) Waiting for completing service (in service) Throughput loss lost sales Limited buffer size Impatient customer In this lecture, we do NOT need the assumption that the average service capacity is higher than average demand rate ( p < ma )! Slide 3 Learning Objectives Understand the characteristics of a loss system Analyze performance measures in a loss system without buffer Understand the impact of buffer on different performance measures in a queuing system Slide 4 Throughput Loss without Buffer ER Example Slide 5 Emergency Room Crowding and Ambulance Diversion Slide 6 Macro Economic Trends Driving Ambulance Diversion Increase in ER visits (14% from 1997 to 2000) 40% of patients admitted through the ER Decrease in number of emergency departments (8.1% decline since 1994) Consequences: Long wait times (see waiting time analysis) Loss of throughput (requires new analysis) 20% of US hospitals are on diversion status for more than 2.4 hours per day Data from L. Green; general accounting office Slide 7 Trauma center moves to diversion status once all servers are busy. Incoming patients are directed to other locations Resources m=3 trauma bays Demand Process One trauma case comes in every 3 hours Service Process Patient stays in trauma bay for an average of 2 hours What is P m , the probability that all m resources are utilized? How often diversion happens? No Buffer! The average interarrival time a = 3 hours/pat CVa = 1 The average service time p = 2 hours/pat Can have any distribution Analyzing Loss Systems Capacity = Demand rate = u = Demand rate Capacity = Slide 8 1 2 3 4 5 0.10 0.0909 0.0045 0.0002 0.0000 0.0000 0.20 0.1667 0.0164 0.0011 0.0001 0.0000 0.25 0.2000 0.0244 0.0020 0.0001 0.0000 0.30 0.2308 0.0335 0.0033 0.0003 0.0000 0.33 0.2500 0.0400 0.0044 0.0004 0.0000 0.40 0.2857 0.0541 0.0072 0.0007 0.0001 0.50 0.3333 0.0769 0.0127 0.0016 0.0002 0.60 0.3750 0.1011 0.0198 0.0030 0.0004 0.67 0.4000 0.1176 0.0255 0.0042 0.0006 0.70 0.4118 0.1260 0.0286 0.0050 0.0007 0.75 0.4286 0.1385 0.0335 0.0062 0.0009 0.80 0.4444 0.1509 0.0387 0.0077 0.0012 0.90 0.4737 0.1757 0.0501 0.0111 0.00200....
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This note was uploaded on 10/16/2011 for the course OM 335 taught by Professor Jonnalagedda during the Fall '08 term at University of Texas at Austin.

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L14_ThroughputLoss_B4 - Slide 1 Lecture 14 Throughput...

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