Expected length of each Queue
Besides service time, it is important to know the number of customers waiting in a queue to be served. It is possible that any customer would change his queue and choose another if find a shorter queue in another parallel server. In general, variability of interarrival and service time causes lines to fluctuate in length. Then question arises, what could be the estimated length of the queue in any server? Some papers describe the general criterion for counting the number of customers in a queue. These counts are a combination of input processes, that are: arrival point process, Poisson counting process (which counts only those units that arrive during the interarrival time and these units are conditionally independent on Poisson interval), and counting group of units being served within the Poisson interval. The above mentioned formula of Lq is defined for average queue length of the queuing system but does not evaluate a length of parallel queues.
Expected length of each Queue Besides service time, it is important to know the number of customers waiting in a queue to be served. It is possible that any customer would change his queue and choose another if find a shorter queue in another parallel server. In general, variability of interarrival and service time causes lines to fluctuate in length. Then question arises, what could be the estimated length of the queue in any server? Some papers describe the general criterion for counting the number of customers in a queue. These counts are a combination of input processes, that are: arrival point process, Poisson counting process (which counts only those units that arrive during the interarrival time and these units are conditionally independent on Poisson interval), and counting group of units being served within the Poisson interval. The above mentioned formula of Lq is defined for average queue length of the queuing system but does not evaluate a length of parallel queues.
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