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    Electronic Resource
    Electronic Resource
    Lattice path counting andM/M/c queueing systems (1995)
    Springer
    Queueing systems 19 (1995), S. 193-214 
    Details
    ISSN: 1572-9443
    Keywords: M/M/c queue ; transient solution ; lattice path counting ; depth of path
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We apply the lattice path counting method to the analysis of the transientM/M/c queueing system. A closed-form solution is obtained for the probability of exactlyi arrivals andj departures within a time interval of lengtht in anM/M/c queueing system that is empty at the initial time. The derivation of the probability is based on the counting of paths from the origin to(i,j) on thexy-plane, that have exactly rd x-steps whose depth from the liney=x isd (d=0,1,...,c−1). The closed-form solution has an expression useful for numerical calculation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01148946
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