On a multilevel controlled bulk queueing system M^X/G^r,R/1

A bulk queueing system under N‐policy with bilevel service delay discipline and start‐up time

“…This result represents a speciM case of M/G,n/1 sudied in Abolnikov/Dshalalow [2], where in our case the modNagion and sate dependency is dropped. (For details see the notion of modulation in [2] or our notice on modulation briefly mentioned ag the end of section 3).…”

“…With the sasne argument as that presented in Model 1, we have that Note that in the case of where the start-up time requirement is dropped, and r = N, the probability generating function P(z) for Model 3 coincides wih gha of the model developed by Abolnikov mad Dshalalow [2]. 6.…”

“…(For details see the notion of modulation in [2] or our notice on modulation briefly mentioned ag the end of section 3). where P0 = ( + ld) Furthermore, if he bulk arrival condition is dropped, i.e., a(z)= z, he probability generating funcgion ca be simplified go" 1 Ab with P0 = N-----This resul agrees wih the M/G/1 queueing system studied by Medhi and Templeton [16].…”

“…Baker An up-to-date extension of the M/G/1 standard system to the class of Npolicy models would include ghe general sgarg-up gime and the N-policy itself. Perhaps the model sgudied in [16] [2] had more flexible inpu and service time dependence han the models under our sudy. However, our models significantly generalize [2] in erms of more versatile service discipline dependencies, namely the three forms of Npolicy.…”

Mathematical Models of Mb/M/1 Bulk Arrival Queueing System

“…Customer arrive service facilities with poison process and exponential service time distribution. Abolnikov et al [8] threw the light on the study a class of bulk queueing systems with a compound Poisson input modulated by semi-Markov process, multilevel control service time and queue length dependent, service delay discipline. Pang and Whitt [9] were motivated by large-scale service systems, and considered an infinite-server queue with batch arrivals, where the service times are dependent within each batch.…”