Effect of Increased Servers Number & Capacity Provisioning to Avoid Loss Problems

Question Description

Need help with my Computer Science question – Im studying for my class.

Problem1:

Effect of Increased Number of Servers

Consider an M/M/k system, where the service rate at each server is ? = 1. Fix system utilization at ? = 0.95. Now increase the number of servers, k, as follows 1, 2, 4, 8, 16, 32 adjusting the arrival rate, ?, accordingly. For each number of servers, derive (i) the fraction of customers that are delayed and (ii) the expected waiting time for those customers who are delayed. We are just looking for numerical answers here. Feel free to write a math program to evaluate the needed summations. Explain the trend that you see

Problem2:

Capacity Provisioning to Avoid Loss

In a call center with k operators, all calls that are not immediately answered by an operator are dropped. Calls arrive according to a Poisson process with rate ? and have Exponentially distributed service times with rate ? = 1. For ? in the set {1, 2, 4, 8}, what should k be as a function of ? to ensure that fewer than 1% of calls are dropped? We are just looking for numerical solutions.

Feel free to write a math program to evaluate the needed summations. When

? doubles, does the needed number of operators double?

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