# Question

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 an exponential distribution with a mean of 15 minutes.

(a) Consider the formulation of this queueing system where the individual shoes (not pairs of shoes) are considered to be the customers. For this formulation, construct the rate diagram and develop the balance equations, but do not solve further.

(b) Now consider the formulation of this queueing system where the pairs of shoes are considered to be the customers. Identify the specific queueing model that fits this formulation.

(c) Calculate the expected number of pairs of shoes in the shop.

(d) Calculate the expected amount of time from when a customer drops off a pair of shoes until they are repaired and ready to be picked up.

(e) Use the corresponding Excel template to check your answers in parts (c) and (d).

(a) Consider the formulation of this queueing system where the individual shoes (not pairs of shoes) are considered to be the customers. For this formulation, construct the rate diagram and develop the balance equations, but do not solve further.

(b) Now consider the formulation of this queueing system where the pairs of shoes are considered to be the customers. Identify the specific queueing model that fits this formulation.

(c) Calculate the expected number of pairs of shoes in the shop.

(d) Calculate the expected amount of time from when a customer drops off a pair of shoes until they are repaired and ready to be picked up.

(e) Use the corresponding Excel template to check your answers in parts (c) and (d).

## Answer to relevant Questions

Identify the customers and the servers in the queueing system in each of the following situations: (a) The checkout stand in a grocery store. (b) A fire station. (c) The tollbooth for a bridge. (d) A bicycle repair shop. (e) ...Consider the E2/M/1 model with λ = 4 and μ = 5. This model can be formulated in terms of transitions that only involve exponential distributions by dividing each interarrival time into two consecutive phases, each having ...A particular work center in a job shop can be represented as a single-server queueing system, where jobs arrive according to a Poisson process, with a mean rate of 8 per day. Although the arriving jobs are of three distinct ...Consider a Jackson network with three service facilities having the parameter values shown below. T (a) Find the total arrival rate at each of the facilities. The jobs to be performed on a particular machine arrive according to a Poisson input process with a mean rate of two per hour. Suppose that the machine breaks down and will require 1 hour to be repaired. What is the ...Post your question

0