The Interrelationship BetweenN-policyM/G/1/KandF-policyG/M/1/KQueues with Startup Time

Abstract

This paper studies the interrelationship between the -N policy M/G/1/K queue and the -F policy G/M/1/K queue. The -N policy queuing problem investigates the most common issue of controlling service. The -F policy queuing problem deals with the most common issue of controlling arrivals. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to develop the solution algorithm for the -N policy M/G/1/K queue with startup time. We have demonstrated that the -N policy M/G/1/K queue with startup time has been effectively used to derive the solution algorithm to the -F policy G/M/1/K queue with startup time. The interrelationship between the -N policy and the -F policy queueing problems are illustrated analytically for 3-stage Erlang (service or interarrival) time distribution.

A survey on queues in machining system: Progress from 2010 to 2017

“…F -policy Shekhar et al [42], Jain and Bhagat [53], Chang et al [70], Kumar and Jain [102], Yang and Wang [105], Jain et al [110], Kuo et al [124].…”

Network Modeling and Performance Analysis under Time-Varying Channel and General Arrival of M2M Services

“…Some researches investigate relationship between M/G/1/K and G/M/1/K queuing systems [5] . To enhance the system performance, Jau-Chuan Ke considered the single vacation model G/M/1/K with N threshold policy [6] ; Mohsin Iftikhar solved the multi-class G/M/1 queuing system with self-similar input and non-preemptive priority [7] . However, all above researches about G/M/1/K queuing model focus on the theoretical analysis and mathematical solutions and there are few people paying close attention to the general arrival distribution of specific services in real networks; On the other hand, at present, the negative exponential distribution is widely used to model the network service time, but the time-varying characteristics of wireless channel makes it impossible to model the service process of wireless network used to bear MTC services accurately.…”

Threshold F-policy and N-policy for multi-component machining system with warm standbys

“…Yang et al (2010) considered the F-policy to study the optimization and sensitivity analysis of a queueing system with single vacation. Kuo et al (2011) demonstrated that the solution algorithm for an F-policy G/M/1/K queue with start-up time can be derived using the N-policy M/G/1/K queue with start-up time. More recently, Jain et al (2012a) studied the effect of different parameters on various performance measures in the M/M/2/K queuing system with (N, F) policy with multi-optional phase repair and start-up.…”