The Concept of Higher Orders Queues in the Queuing Theory

Abstract

The paper considers various types of queues arising in queuing systems. The concept of an N-th order queue is introduced; the calculation algorithm of the first and second moments of main discrete and continuous random variables characterizing behavior of higher orders queues in queuing systems of the mixed type is presented. AMS Subject Classification: 60K25Key Words: physical queue, real queue, quality of service (QoS), queuing system (QS) Main DefinitionsAn N-th order queue will be called the queue calculated in case when there are m+N claims in the system as minimum, and N of them are in the memory. Such a queue exists if a newly arrived claim finds a minimum N claims waiting for service before this one.At N=0 we have a physical queue which is explicitly studied in the work [7]. In the system of GPSS World simulation modeling this characteristic has the name "a queue without zero inputs".At N=1 we have the so-called real queue; at N>1 we have queues of higher orders.

simulation-based approach for minimizing waiting time in AIIMS, Delhi using Queuing model

“…The analysis of waiting time in healthcare systems can be approached mathematically using queuing theory (Rotich, 2016). Queuing theory is a classical approach that has been employed to gain insight into hospital processes since the 1950s (Lee et al, 1997;Titovtsev, 2016). An ineffective and inefficient appointment system is one of the main issues for the long waiting time of patients in an outpatients department.…”

Generalized Little's Formulas and Classification of Higher Orders Queues in the Queuing Theory

“…Let us remind that we have called the N-th order queue as the queue that is calculated as long as there is a minimum of m+N claims in the system; N of them is in the memory [4]. Such queue exists if a newly arrived claim finds a minimum claims N waiting for service before it.…”

“…It was found out in works [1], [2] and [4], that for systems of M/M/m and M/M/m/E classes (though, all numerical characteristics of the first ones can be obtained by a limit transference from numerical characteristics of the second ones) the following relation is performed…”