Queueing Analysis: Discrete-time systemsNorth-Holland, 1991 - Queuing theory |
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Page 25
... 1st slot . The case in ( 1.68 ) occurs if a new service is started at the beginning of the n + 2nd slot for one of the messages that arrive during the n + 1 st slot . The case in ( 1.69 ) occurs if the service in the n + 1st slot is ...
... 1st slot . The case in ( 1.68 ) occurs if a new service is started at the beginning of the n + 2nd slot for one of the messages that arrive during the n + 1 st slot . The case in ( 1.69 ) occurs if the service in the n + 1st slot is ...
Page 27
... slots ) in the n + 1st slot as the time that a supermessage would wait in the corresponding Geo / G / 1 system with FCFS discipline if it arrived in the n + 1st slot ; let us refer to Figure 6.2 on page 24. The waiting time of a ...
... slots ) in the n + 1st slot as the time that a supermessage would wait in the corresponding Geo / G / 1 system with FCFS discipline if it arrived in the n + 1st slot ; let us refer to Figure 6.2 on page 24. The waiting time of a ...
Page 115
... 1st slot leaving the system empty . The case in ( 3.89 ) occurs if the vacation in the n + 1st slot is continued to ... 1 ) ( 1 ) = 6.3 Exhaustive Service Systems with Vacations I 115.
... 1st slot leaving the system empty . The case in ( 3.89 ) occurs if the vacation in the n + 1st slot is continued to ... 1 ) ( 1 ) = 6.3 Exhaustive Service Systems with Vacations I 115.
Common terms and phrases
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