An M/M/∞ queueing system is similar to an M/M/1 system except that it has infinitely many servers. Therefore, all customers will be served upon arrival, and there will not be a queue. Examples of...

An M/M/∞ queueing system is similar to an M/M/1 system except that it has infinitely many servers. Therefore, all customers will be served upon arrival, and there will not be a queue. Examples of infinite-server systems are service facilities that provide self-service such as libraries. Consider an M/M/∞ queuing system in which customers arrive according to a Poisson process with rate λ, and service times are exponentially distributed with mean 1/λ. Find the long-run probability mass function and the expected value of the number of customers in the system.