Physical and Mathematical Queues in the Applied Queuing Theory

Abstract

The problem of various types of queues arising in queuing systems is considered in the paper. The concept of a physical queue is introduced; universal mathematical formulas of the first and second moments of main discrete and continuous random variables characterizing behavior of physical queues for various models of mixed type queuing systems are obtained.

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

“…As it is shown in the work [3], corresponding relations have quite a similar form (1) for a physical queuet however this formula becomes unjust for higher orders queues.…”

“…Such queue exists if a newly arrived claim finds a minimum claims N waiting for service before it. When N=0 we have a physical queue which is studied in work [3] in detail. In the GPSS World simulation modeling system this characteristic has the name "queue without zero inputs".…”

The Concept of Higher Orders Queues in the Queuing Theory

“…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".…”

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

“…These appointment systems were tested for punctual patients as well as for no-shows. Kirpichnikov and Titovtsev (2016) provide particularly focused on identifying multiple elements which led to long queues and testing different appointment systems to identify an optimal system. Bako et al (2017) developed a model of determining optimal rules for an outpatient appointment system.…”