A multiserver queue with narrow- and wide-band customers and wide-band restricted access

We consider a multiserver queueing system with two classes of customers: a type 1 (narrow-band, NB) customer requires a single server, while each type 2 (wide-band, WB) customer requests n of the rn servers (n is not random). Servers allocated to a type 2 customer are seized and released simultaneously. Service times are exponentially distributed with mean l/p, for type i customers (i = 1,2). Blocked type 1 customers are cleared while blocked type 2 customers may be delayed in an infinite waiting room. A type 1 customer enters service immediately upon arrival if at least one server is free, irrespective of the status of the type 2 queue. WB customers have restricted access to the service facility; a cutoff parameter specifies the maximum number of type 2 customers that can be in service at the same time. Two approaches, moment-generating functions and matrix-geometric techniques, are considered for the computation of the system performance; that is, the mean waiting time in queue and the probability of delay (i.e., nonzero waiting time) for type 2 customers, as well as the probability of blocking for type 1 customers.