Consider the M/M/s queue and denote by X(t) the number of customers in the system at...

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Consider the M/M/s queue and denote by X(t) the number of customers in the system at time t. a) Determine explicit expressions for the long-term probability To that there is no customer in the system for the case s = 2. Plot 1 - To and the queue length L as a %3D function of the traffic intensity p = where A and u denote arrival rate and service rate, respectively. b) Determine the mean waiting time W for an M/M/2 system when 2 = 2 and u = 1.2. Compare this with the mean waiting time in an M/M/1/ system whose arrival rate is H = 1.2. Why is there a difference when the arrival rate per server is the same in both cases? Consider the M/M/s queue and denote by X(t) the number of customers in the system at time t. a) Determine explicit expressions for the long-term probability To that there is no customer in the system for the case s = 2. Plot 1 - To and the queue length L as a %3D function of the traffic intensity p = where A and u denote arrival rate and service rate, respectively. b) Determine the mean waiting time W for an M/M/2 system when 2 = 2 and u = 1.2. Compare this with the mean waiting time in an M/M/1/ system whose arrival rate is H = 1.2. Why is there a difference when the arrival rate per server is the same in both cases?

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