Performance Measure Equation Average number in line (18–6) H(H – 1) (-) Probability of zero units in the system Po= 1- (18–7) Probability of n units in the system P,= Po (18–8a) --G)' Probability of less than n units in the system P = (18–8b) I This notation is commonly used to specify waiting-line models. The first symbol refers to arrivals, the second to service, and the third to the number of servers. M stands for a rate that can be described by a Poisson distribution or, equivalently, a time that can be described by an exponential distribution. Hence, M/M/1 indicates a Poisson arrival rate, a Poisson service rate, and one server. The symbol D is used to denote a deterministic (i.e., constant) service rate. Thus the notation M/D/1 would indicate the arrival rate is Poisson and the service rate is constant. Finally, the notation M/M/S would indicate multiple servers.

Performance Measure Equation Average number in line (18–6) H(H – 1) (-) Probability of zero units in the system Po= 1- (18–7) Probability of n units in the system P,= Po (18–8a) --G)' Probability of less than n units in the system P = (18–8b) I This notation is commonly used to specify waiting-line models. The first symbol refers to arrivals, the second to service, and the third to the number of servers. M stands for a rate that can be described by a Poisson distribution or, equivalently, a time that can be described by an exponential distribution. Hence, M/M/1 indicates a Poisson arrival rate, a Poisson service rate, and one server. The symbol D is used to denote a deterministic (i.e., constant) service rate. Thus the notation M/D/1 would indicate the arrival rate is Poisson and the service rate is constant. Finally, the notation M/M/S would indicate multiple servers.

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 27P

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