GI|M/M/c queue with multiple acceptances in a window

We consider a queue with arrival acceptance windows in which multiple customers can enter the system in a window. Each customer is assigned to arrive at the system within a time interval, called acceptance window. A customer who does not arrive at the system within his assigned window cannot be offered the service and is lost. The delay time of a customer is the length of time interval from the epoch at which the window is generated to the actual arrival time of the customer. The delay times of customers are assumed to be independent and exponentially distributed with common parameter υ. There are c parallel servers and each service time is exponentially distributed with parameter μ. For this model, we derive the queue length distribution and waiting time distribution in equilibrium.