On an M/G/1 queue providing general first essential service with customer's choice for general or deterministic second optional service.

We study an M/G/1 queuing system with one by one Poisson arrivals and one by one general first essential service followed by one of the two types of second optional heterogeneous services. A customer entering the service channel compulsorily goes through first essential service. After completion of the first service, the customer has the option to take a second optional service with probability π or no second optional service with probability 1−π. If the customer decides to take the second optional service, he may take a general second optional service with probability a1 or a deterministic second optional service with probability a2, a1 + a2 = 1. We find steady state solution in terms of the generating function of the queue length as well as the explicit steady state probabilities for various states of the system. Results for a few interesting special cases are derived. [ABSTRACT FROM AUTHOR]