Question

1. A system of N servers has an arrival rate of 400 requests per second. The performance requirement is that the probability of an arriving job waiting is at most 0.2. The processing times are exponentially distributed with mean 1 second. (a) How many servers would be required using N M/M/1 queues in parallel, where an arrival is equally likely to join any of the N queues? (b) How many servers would be required using an M/M/N model (use the exact model, not the square root rule)? (c) How many servers does the square root rule suggest?

          1. A system of N servers has an arrival rate of 400 requests per second. The performance
requirement is that the probability of an arriving job waiting is at most 0.2. The processing
times are exponentially distributed with mean 1 second.
(a) How many servers would be required using N M/M/1 queues in parallel, where an
arrival is equally likely to join any of the N queues?
(b) How many servers would be required using an M/M/N model (use the exact model,
not the square root rule)?
(c) How many servers does the square root rule suggest?

1. A system of N servers has an arrival rate of 400 requests per second. The performance
requirement is that the probability of an arriving job waiting is at most 0.2. The processing
times are exponentially distributed with mean 1 second.
(a) How many servers would be required using N M/M/1 queues in parallel, where an
arrival is equally likely to join any of the N queues?
(b) How many servers would be required using an M/M/N model (use the exact model,
not the square root rule)?
(c) How many servers does the square root rule suggest?

Added by Inmaculada M.

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