Question

Consider an ergodic $M / M / s$ queue in steady state (that is, after a long time) and argue that the number presently in the system is independent of the sequence of past departure times. That is, for instance, knowing that there have been departures $2,3,5$, and 10 time units ago does not affect the distribution of the number presently in the system.

Name: Consider an ergodic M / M / s queue in steady state (that is, after a long time) and argue that the number presently in the system is independent of the sequence of past departure times. That is, for instance, knowing that there have been departures 2,3,5, and 10 time units ago does not affect the distribution of the number presently in the system.
Uploaded: 2021-12-14T06:27:20-08:00
Duration: 46 s
Channel: Ameer Said
Description: Consider an ergodic M / M / s queue in steady state (that is, after a long time) and argue that the number presently in the system is independent of the sequence of past departure times. That is, for instance, knowing that there have been departures 2,3,5, and 10 time units ago does not affect the distribution of the number presently in the system.

          Consider an ergodic $M / M / s$ queue in steady state (that is, after a long time) and argue that the number presently in the system is independent of the sequence of past departure times. That is, for instance, knowing that there have been departures $2,3,5$, and 10 time units ago does not affect the distribution of the number presently in the system.

Added by Kristen K.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Ameer Said

12/14/2021

Step 1

This means that the system has no memory of past events and is independent of the sequence of past departure times. Show more…

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Consider an ergodic $M / M / s$ queue in steady state (that is, after a long time) and argue that the number presently in the system is independent of the sequence of past departure times. That is, for instance, knowing that there have been departures $2,3,5$, and 10 time units ago does not affect the distribution of the number presently in the system.