only for question 2

A Single-Server Queue Suppose that customers arrive at a single-server system in accordance with a Poisson process with rate 1. Upon arriving a customer must pass through a door that leads to the server. However, each time someone passes through, the door becomes locked for the next t units of time. An arrival finding a locked door is lost, and a cost c is incurred by the system. An arrival finding the door unlocked passes through to the server. If the server is free, the customer enters service; if the server is busy, the customer departs without service and a cost K is incurred. If the service time of a customer is exponential with rate y, find the average cost per unit time incurred by the system. 2. (10 points) Recall the single-server queue example covered in the lecture. Find the long-run proportion of time that the server is busy. A Single-Server Queue Suppose that customers arrive at a single-server system in accordance with a Poisson process with rate 1. Upon arriving a customer must pass through a door that leads to the server. However, each time someone passes through, the door becomes locked for the next t units of time. An arrival finding a locked door is lost, and a cost c is incurred by the system. An arrival finding the door unlocked passes through to the server. If the server is free, the customer enters service; if the server is busy, the customer departs without service and a cost K is incurred. If the service time of a customer is exponential with rate y, find the average cost per unit time incurred by the system. 2. (10 points) Recall the single-server queue example covered in the lecture. Find the long-run proportion of time that the server is busy