COMPUTATION OF PACKET RESPONSE-TIME VIA LAGRANGE SERIES EXPANSION

Packets are processed in bulk at the nodes of a computer communication network. A complete analytical solution of the packet response time i n a node processor is derived. The node processor is modelled as an M/ M([K])/1 queue. In this queue, the packets arrive according to a Poiss on process, and the service times are exponentially distributed. In ea ch service period the number of packets served is the minimum of K and the number of packets present in the queue. In existing literature it is assumed implicitly that a root of a polynomial equation, lying in the interval (0, 1), will be evaluated numerically. A Lagrange series expansion of a root of this polynomial equation of degree (K+1) is der ived. The proposed solution technique can be used for evaluating analy tically other Markovian bulk service queues, and also the E,/M/1 queue .