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.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 70P
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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)”.
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