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

A multiserver queueing system with two classes of customers is considered: a type-1 (narrowband, NB) customer requires a single server, while each type-2 (wideband, WB) customer requests n of the m servers (n is not random). Severs allocated to a type-2 customer are seized and released simultaneously. Service times are exponentially distributed with mean 1/_μi 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