Case #3 of Queueing Theory Prob Set 15.6E #5McBurger fastfood has 3 cashiers. Customers arrive accd'g to a Poisson distribution every 3 mins andform one line to be served by the first available cashier. The time to fill an order is exponentiallydistributed with a mean of 5 mins. The waiting room inside the restaurant is limited. However, the food isgood, and customers are willing to line up outside the restaurant, if necessary. Determine the size of thewaiting room inside the restaurant (excluding those at the cashiers) such that the probability that anarriving customer does not wait outside the restaurant is at least 0.999.

Arrival time = 3 minsService time = 5 minsNumber of cashiers = 3

Answered: McBurger fastfood has 3 cashiers.…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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Twelve customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from 11-2 p.m. on weekdays. It takes Andy a mean time of 4 minutes to fill each order (following a negative exponential distribution). The Waiting La λ Line Table is provided below and also we know that W₁ = Table: Average Number of Customer in Waiting Line P .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .30 .55 60 .65 .70 .75 .80 .85 .90 .95 1.0 1.2 1.4 1.6 1.8 2.0 Poisson Arrivals, Exponential Service Times Number of Service Channels, M 2 3 4 1 .0111 .0264 .0500 .0833 .1285 .1884 .2666 .3681 .5000 .6722 3000 .6722 .9000 1.2071 1.6333 2.2500 3.2000 4.8166 8.1000 18.0500 .0008 .0020 .0039 .0069 .0110 .0166 .0239 .0333 .0449 0333 .0449 .0593 .0767 .0976 .1227 .1523 .1873 2285 .2767 .3333 .6748 1.3449 2.8444 7.6734 .0019 .0030 .0043 0030 .0043 .0061 .0084 .0112 .0147 .0189 0239 .0300 .0371 .0454 .0904 .1778 .3128 .5320 .8888 .0031 .0041 .0053 .0067 .0158 .0324…
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Q5
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