A wide-band ISDN provides access to many different users in a shared fashion. Control of the available bandwidth allocation is necessary for efficiency and flexibility. In this paper, the system is modelled as a multiple-server multiple-queue system, where access requests require service from a random number of servers. Requests are generated by a finite number of sources. Each request is entered in a queue so that the queue index indicates the bandwidth needed by the request (in basic bandwidth units). Control of service allocation is accomplished by assigning priorities to queues. Two priority types are examined here, where relatively higher priority is assigned to requests in the smaller indexed or the larger indexed queues. When more than one request can be served due to the availability of bandwidth, the one with the highest priority is chosen first, The procedures that regulate the bandwidth allocation are described, and a Markov-chain based solution to the model is developed to produce the system state probabilities, and utilization and performance measures.