Queueing theoryВ is the statistical study of waiting lines, or lines.[1]В In queueing theory a model is constructed in order that queue lengths and waiting times may be predicted.[1] Queueing theory started out with analysis byВ Agner Krarup ErlangВ when this individual created models to describe the Copenhagen cell phone exchange.[1]В The tips have seeing that seen applications includingtelecommunications,[2]В traffic architectural, В computing[3]В and the appearance of factories, shops, offices and hospitals.[4] ContentsВ В[hide]В * 1В Overview * 2В History * 3В Application to telephony * 4В Queueing networks 5. 5В Utilization 5. 6В Role of Poisson procedure, exponential droit * 7В Limitations of queueing theory 5. 8В See likewise * 9В References * 10В Further reading 2. 11В External links| -------------------------------------------------

[edit]Overview

The wordВ queueВ comes, viaВ French, via theВ LatinВ cauda, meaning tail. The spelling " queueing" more than " queuing" is typically encountered in the educational research field. In fact , one of many flagship magazines of the occupation is namedВ Queueing Systems. Queueing theory is generally considered a branch ofВ operations researchВ because the results are frequently used when making organization decisions about the resources necessary to provide support. It is relevant in a wide array of situations that will be encountered in corporate, commerce, sector, healthcare,[5]В public service and engineering. Applications are usually encountered incustomer serviceВ situations as well asВ transportВ andВ telecommunication. Queueing theory is definitely directly applicable toВ intelligent vehicles systems, В call centers, В PABXs, В networks, telecommunications, В serverВ queueing, В mainframeВ computerВ of telecommunications terminals, advanced telecommunications systems, andВ traffic flow. Notation for talking about the characteristics of aВ queueing modelВ was first advised byВ David G. KendallВ in 1953. В Kendall's notationВ introduced an A/B/C queueing mention that can be found in every standard contemporary works on queueing theory, for instance , Tijms.[6] The A/B/C mention designates a queueing program having A while interarrival time distribution, B as services time distribution, and C as number of servers. For instance , " G/D/1" would reveal a General (may be anything) arrival process, a Deterministic (constant time) service procedure and a single server. More information on this note are given inside the article aboutВ queueing models. -------------------------------------------------

[edit]History

Agner Krarup Erlang, aВ DanishВ engineer who have worked pertaining to the Copenhagen Telephone Exchange, published the first paper on queueing theory in 1909.[7][8][9]В He modeled the number of telephone calls arriving at a great exchange by aВ Poisson processВ and solved theВ M/D/1 queueВ in 1917 andВ M/D/k queueingВ model in 1920.[10] Felix PollaczekВ solved theВ M/G/1 queueВ in 1930, a simple solution later recast in probabilistic terms byВ Aleksandr Khinchin.[10]В AfterВ World Conflict IIВ queueing theory became a location of analysis interest to mathematicians.[10] David G. KendallВ introduced an A/B/C queueing mention in 1953. Work on queueing theory utilized in modernВ packet switchingВ networks was performed in the early on 1960s byВ Leonard Kleinrock. -------------------------------------------------

[edit]Application to telephony

The public switched cell phone network (PSTN) was created to accommodate the offered targeted traffic intensity with only a small loss. The performance of loss systems is quantified by their grade of assistance, driven by assumption that if sufficient capacity is usually not available, the phone call is rejected and dropped.[11] Alternatively, overflow systems make use of alternative routes to change calls by way of different paths — possibly these systems have a finite traffic having capacity.[11] Yet , the use of queueing in PSTNs allows the systems to queue all their customers' requests until totally free resources available. This means that if traffic strength levels go over available potential, customer's cell phone calls are not misplaced;...