Consider the M/M/1 queueing system with arrival rate λ > 0 and service rate μ > 0. (a) Compute the expected number of arrivals during a service time (also called service period). (b) Compute the probability that no customers arrive during a service period. You may use the trick of computing expectation/probability by conditioning, i.e., “unconditional expectation (or probability) is equal to the expectation of conditional expectation (or probability)”.

Consider the M/M/1 queueing system with arrival rate λ > 0 and service rate μ > 0. (a) Compute the expected number of arrivals during a service time (also called service period). (b) Compute the probability that no customers arrive during a service period. You may use the trick of computing expectation/probability by conditioning, i.e., “unconditional expectation (or probability) is equal to the expectation of conditional expectation (or probability)”.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.4: Important Queueing Relationships

Problem 6P

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