A mixed service for two queue gated vacation with Bernoulli schedule policy

In this paper we discuss two queue gated vacation system with Bernoulli schedule. In a gated service system, when the server returns from second queue, a logical gate is closed so that the server accepts and serves only those customers present at that instant before the gate. The service cycle is defined as time interval between two subsequent visit of first queue. The Bernoulli schedule is applied to the first queue at the end of service period. The modified service policy is described as, either the gate reopens at the end of the service period of type-1 customers with probability 1-p, or, the server may start serving type-2 customers with probability p. For type-2 customers we follow the normal gated policy. We have derived Z-transform (PGF) of joint queue length distribution at the polling beginning epoch and Laplace-Stieltjes Transform (LST) of distribution of service cycle for type-1 customers.