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Performance analysis: Other performance measures

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• Other performance measures: Idle time/busy time
  • How often do you waste system resources: Idle system

    The system is idle when there are zero (0) customers in the system The fraction of time that the system is idle is equal to the probability that the system is empty Therefore: fraction of time that system is idle = Ҏ[ 0 custumer in system ] = p0 The fraction of time that an M/M/1 queue is idle is equal to: fraction of time that M/M/1 queue is idle = 1 - ρ

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  • Busy system: (busy = not idle)

    The system is idle when there are not zero (0) customers in the system The fraction of time that the system is idle is equal to the probability that the system is not empty Therefore: fraction of time that system is idle = 1 - Ҏ[ 0 custumer in system ] = 1 - p0 The fraction of time that an M/M/1 queue is busy is equal to: fraction of time that M/M/1 queue is idle = ρ

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• Other performance measure: loaded system
  • The M/M/*/k queueing model is used to model system with finite waiting capacity (the maximum number of customers in the system is at most k)

  • We can ask the following capacity question on system with finite waiting capacity:

    How often is the system running at system capacity I.e., how often is the number of customers in the system equal to its maximum

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  • The fraction of time that an M/M/*/k queueing system is running at maximum capacity can be computed as:

    fraction of time that M/M/*/k system is at max. cap. = Ҏ[ k customors in system ] = pk