%0 Journal Article
%T Combinatorial approach to M/M/1 queues using hypergeometric functions
%A J. Saran
%A K. Nain
%J International Mathematical Forum
%D 2013
%I 
%X In this paper we use a well known reflection principle for lattice path countingto apply for the analysis of the M/M/1 queuing system. The joint distribution of iarrivals and j departures over a time interval of length t is obtained, when there are kcustomers in the beginning of the system. The derivation uses the lattice pathapproach between two points, in two dimensional x-y plane with certain restrictions.Finally a known result of queue length is verified from Satty (1961).
%K M/M/1 queues
%K Combinatorial Method
%K Lattice Path
%K Idle period
%K Bessel¡¯s function
%K Hypergeometric Functions
%U http://www.m-hikari.com/imf/imf-2013/9-12-2013/saranIMF9-12-2013.pdf