Queueing Analysis: Discrete-time systemsNorth-Holland, 1991 - Queuing theory |
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1st slot arbitrary message arbitrary slot boundary boundary is given busy period process busy period started defined delay cycle denotes the number discrete-time E[W]LCFS early arrival model elapsed service FCFS system FDMA Geo/G/1 system Hence idle period initial condition joint distribution joint PGF Kronecker's delta late arrival model LCFS Markov chain mean waiting measured in slots message of class messages arrive messages that arrive multiple vacation model Note nth slot number of messages number of packets P₁ packet model PGF P(z PGF W(u Po(w Po(z priority queues Prob Prob[L probability queue size immediately recurrence relation remaining service Rouché's theorem semi-Markov process service completion service cycle service facility service period service time immediately setup steady-state Substituting supermessage of class system immediately system is empty system is given system without vacations time-dependent process vacation period Wg(u wɅ(z Πο Σ Π Σ Σ ΣΠ