Discussion
In terms of the usual notation, for an M|M|1 queueing system, which of the following equations does not hold ?
Answer: B
The equation that does not hold is \(W_{q} = W_{s}\).
In an M/M/1 queue a customer's time in the system is the waiting time in the queue plus the service time, so
\[ W_{s} = W_{q} + \frac{1}{\mu} \]
which makes \(W_{s}\) strictly larger than \(W_{q}\). The two are never equal.
The other three are standard M/M/1 results: \(L_{s} = \rho/(1 - \rho)\) with \(\rho = \lambda/\mu \lt 1\); \(W_{s} = W_{q} + 1/\mu\) as above; and \(L_{q} = \lambda W_{q}\), Little's law applied to the queue.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development