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.
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.
The paper presents a mathematical model of an open multi-channel queuing system having m service facilities of identical efficiency with exponentially distributed service time. The input stream of Poisson character includes demands of different types arriving from an arbitrary quantity of sources h and having various size-limited queues, at the same time intervals between the nearest-neighbor limits are equal to the unit everywhere. General mathematical formulae for probabilistic characteristics, as well as for the first and second moments of numerical characteristics specifying the quality of service in a steady-state mode of work have been obtained.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.