Lecture#14 Methods of the queuing theory The Bonch-Bruevich Saint-Petersburg State University of Telecommunications Series of lectures “Telecommunication networks” Instructor: Prof. Nikolay Sokolov,

Origin of the teletraffic theory In the beginning of XX century telephone networks began to develop actively. New problems of these networks planning have arisen. One of the first problems lied in the channels bundle capacity calculation for given loss probability. A.K. Erlang has derived formula which allowed solution of this problem. It is considered, that development of the teletraffic theory has begun exactly from the works of Erlang. The name "Erlang" was given for the traffic intensity unit in 1946 by CCIF (predecessor to ITU- T). First switching systems operated according to algorithm with losses. This means that in the absence of unoccupied serving device the call is lost. Utilization of the program control permitted to introduce service discipline with waiting. This has increased efficiency of the call serving. Wide application of this algorithm has led to interchange of word combination "teletraffic theory“ with “queuing theory”. At the present time, queuing theory is widely applied in the researches of telecommunications networks, transport systems, trade and retail field.

Classification of the queueing models (1)

Classification of the queueing models (2)

Classification of the queueing models (3)

Systems with losses Y – traffic, V – number of channels, P – loss probability. If V =1:

The mean number of incoming calls (1)

The mean number of incoming calls (2)

Flow of incoming calls

The mean holding time (1)

The mean holding time (2)

The carried traffic as a function of time

Busy hour

The carried traffic as a function of time The most important characteristics of queueing system for the telecommunications network planning are: mean value of the delay time, quantile of the delay distribution functions. Exactly these two characteristics are standardized in ITU-T recommendations and ETSI standards. For solution of other problems not included in the network planning process, other characteristics of queueing system are of interest.

Main formulas (1)

Main formulas (2)

Main formulas (3)

Main formulas (4)

Mean delay time

ITU-T Recommendation Y.1541 (1)

ITU-T Recommendation Y.1541 (2)

ITU-T Recommendation Y.1541 (3)

ITU-T Recommendation Y.1541 (4)

ITU-T Recommendation Y.1542 (1)

ITU-T Recommendation Y.1542 (2)

ITU-T Recommendation Y.1542 (3)

Instructor: Prof. Nikolay Sokolov, Questions? Methods of the queuing theory