# Question: Consider the M M s model a Suppose there is one server and

Consider the M/M/s model.

(a) Suppose there is one server and the expected service time is exactly 1 minute. Compare L for the cases where the mean arrival rate is 0.5, 0.9, and 0.99 customers per minute, respectively. Do the same for Lq, W, Wq, and P{W > 5}. What conclusions do you draw about the impact of increasing the utilization factor p from small values (e.g., p = 0.5) to fairly large values (e.g., p = 0.9) and then to even larger values very close to 1 (e.g., p = 0.99)?

(b) Now suppose there are two servers and the expected service time is exactly 2 minutes. Follow the instructions for part (a).

(a) Suppose there is one server and the expected service time is exactly 1 minute. Compare L for the cases where the mean arrival rate is 0.5, 0.9, and 0.99 customers per minute, respectively. Do the same for Lq, W, Wq, and P{W > 5}. What conclusions do you draw about the impact of increasing the utilization factor p from small values (e.g., p = 0.5) to fairly large values (e.g., p = 0.9) and then to even larger values very close to 1 (e.g., p = 0.99)?

(b) Now suppose there are two servers and the expected service time is exactly 2 minutes. Follow the instructions for part (a).

## Answer to relevant Questions

Consider the M/M/s model with a mean arrival rate of 10 customers per hour and an expected service time of 5 minutes. Use the Excel template for this model to obtain and print out the various measures of performance (with t ...Derive Wq directly for the following cases by developing and reducing an expression analogous to Eq. (1) in Prob. 17.6-17. (a) The M/M/1 model (b) The M/M/s model Consider a telephone system with three lines. Calls arrive according to a Poisson process at a mean rate of 6 per hour. The duration of each call has an exponential distribution with a mean of 15 minutes. If all lines are ...Consider the M/G/1 model. (a) Compare the expected waiting time in the queue if the servicetime distribution is (i) exponential, (ii) constant, (iii) Erlang with the amount of variation (i.e., the standard deviation) halfway ...Consider a single-server queueing system with a Poisson input, Erlang service times, and a finite queue. In particular, suppose that k = 2, the mean arrival rate is 2 customers per hour, the expected service time is 0.25 ...Post your question