# Question

Marsha operates an expresso stand. Customers arrive according to a Poisson process at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 75 seconds.

(a) Use the M/G/1 model to find L, Lq, W, and Wq.

(b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and Wq.

(c) What is the ratio of Lq in part (b) to Lq in part (a)?

(d) Use trial and error with the Excel template for the M/G/1 model to see approximately how much Marsha would need to reduce her expected service time to achieve the same Lq as with the expresso vending machine.

(a) Use the M/G/1 model to find L, Lq, W, and Wq.

(b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and Wq.

(c) What is the ratio of Lq in part (b) to Lq in part (a)?

(d) Use trial and error with the Excel template for the M/G/1 model to see approximately how much Marsha would need to reduce her expected service time to achieve the same Lq as with the expresso vending machine.

## Answer to relevant Questions

Antonio runs a shoe repair store by himself. Customers arrive to bring a pair of shoes to be repaired according to a Poisson process at a mean rate of 1 per hour. The time Antonio requires to repair each individual shoe has ...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 ...Consider a single-server queueing system with any servicetime distribution and any distribution of interarrival times (the GI/G/1 model). Use only basic definitions and the relationships given in Sec. 17.2 to verify the ...Under the assumptions specified in Sec. 17.9 for a system of infinite queues in series, this kind of queueing network actually is a special case of a Jackson network. Demonstrate that this is true by describing this system ...Suppose that a queueing system has two servers, an exponential interarrival time distribution with a mean of 2 hours, and an exponential service-time distribution with a mean of 2 hours for each server. Furthermore, a ...Post your question

0