QUEUING ANALYSIS: BIRTH AND DEATH PROCESS

A store has two clerks, each capable of serving customers at an average rate of 60 per hour, actual service times are exponentially distributed. The capacity of the store is five customers, with no waiting outside allowed. Customers come to the store in a Poisson-type process where the average arrival rate depends on the number of people in the store, as follows: 5 0 2 3 4 Number in store Average arrival rate, h 200 100 110 120 140 170 1 a) Determine the expected number of customers in the store together. b) Determine the expected amount of time a customer must wait for service. c) Determine the expected rate at which customers are lost due to limited facilities. A store has two clerks, each capable of serving customers at an average rate of 60 per hour, actual service times are exponentially distributed. The capacity of the store is five customers, with no waiting outside allowed. Customers come to the store in a Poisson-type process where the average arrival rate depends on the number of people in the store, as follows: 5 0 2 3 4 Number in store Average arrival rate, h 200 100 110 120 140 170 1 a) Determine the expected number of customers in the store together. b) Determine the expected amount of time a customer must wait for service. c) Determine the expected rate at which customers are lost due to limited facilities