Parallel queues with multiple servers: effect of queue selection and service time distribution on the allocation of bandwidth in communication networks

摘要

A queueing system is examined where customers must be allocated a variable number of servers, out of a fixed total, before they can enter service. Systems of this type appear in situations where service is provided in units and each customer declares the needed number of units upon entry to the system. An important application of this analysis is in bandwidth allocation of wide-band integrated service digital communication networks. Other examples include transportation systems, allocation of processors in multiprocessor systems and buffers in memory, and allocation of resources in battle and other military applications. The system is modeled as a multiple-server multiple-queue system, where customers (communication requests) require service from a random number of servers (bandwidth units). Each customer enters a queue so that the queue index indicates the number of servers needed by the customer. Queue selection probabilities and service times depend on the queue index. To achieve efficiency and flexibility, control of the available server allocation is accomplished by assigning priorities to queues. When more than one customers can be served due to the availability of servers, higher priority may be assigned to customers in the smaller indexed or the larger indexed queues. The procedures that regulate the server 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.