Pseudo-conservation laws in cyclic-service systems

Abstract

This paper considers single-server, multi-queue systems with cyclic service. Non-zero switch-over times of the server between consecutive queues are assumed. A stochastic decomposition for the amount of work in such systems is obtained. This decomposition allows a short derivation of a 'pseudoconservation law' for a weighted sum of the mean waiting times at the various queues. Thus several recently proved conservation laws are generalised and explained.

Analysis and performance comparison of uniform and mixed service policy for vacation queue

“…The behavior is expected as we have considered the completion time for type-L and type-2 customers instead of their service time duration. We have seen in [10] that the priority queueing follows a reservation law. We can achieve increase in delay/throughput for one type of customer at the cost of decreasing delay/throughput for another type of customer.…”

Distribution of the workload in multiclass queueing systems with server vacations

“…The workload decomposition in (2) for single-server multiclass systems (Boxma and Groenendjik [2] and Boxma [l]) was initially derived in an attempt to interpret, unify, and generalize the pseudoconservation laws of Ferguson and Aminetzah [4] and of Watson [12]. Calculating the mean workload from (2) indeed easily leads to those conservation laws, as special cases of a much more general pseudoconservation law. However, (2) has until now not been exploited to obtain insight into the workload distribution of single-server multiclass systems with vacations (switchover times).…”

“…The purpose of this paper is to give Y*(s) for systems with setup times (Section 3) and for polling systems (Section 4), thus obtaining the LST of the DF for the workload in those systems by (2). For general systems with nonpreemptive service, the evaluation of the mean workload E [ U] leads to the so-called pseudoconservation law with respect to the traffic-intensity-weighted sum of the mean waiting times for each class of customers (see Section 2), which has been studied for several polling systems.…”

“…39, pp. 41-52 (1992) For a broad category of multiclass queueing systems with server vacations, including the above-mentioned systems considered in this paper, Boxma and Groenendijk [2] (see also Boxma [l]) established the following work decomposition result. The steady-state workload U is distributed as the sum of the steady-state workload U,,,,, in the corresponding MIGI1 system without vacations and the steady-state workload Y in the original system at an arbitrary time during a vacation period: Furthermore, U,,,,, and Yare independent.…”

Improving the Performance of Polling Models Using Forced Idle Times

“…We show how to derive Theorems 1 and 2 which are based on a decomposition principle from [5] and on the technique of the proofs of Theorems 1 and 8 from [4]. We mention that the proofs of Theorems 1 and 2 are quite standard and that the key novelty is the computation of the parameter-dependent quantities in Section 3.2.…”