In queueing theory, a discipline within the mathematical theory of probability, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953 where A denotes the time between arrivals to the queue, S the service time distribution and c the number of service channels open at the node. It has since been extended to A/S/c/K/N/D where K is the capacity of the queue, N is the size of the population of jobs to be served, and D is the queueing discipline.
When the final three parameters are not specified (e.g. M/M/1 queue), it is assumed K = ∞, N = ∞ and D = FIFO.
A M/M/1 queue means that the time between arrivals is Markovian (M), i.e. the inter-arrival time follows an exponential distribution of parameter λ. The second M means that the service time is Markovian: it follows an exponential distribution of parameter μ. The last parameter is the number of service channel which one (1).
In this section, we describe the parameters A/S/c/K/N/D from left to right.
A code describing the arrival process. The codes used are:
This gives the distribution of time of the service of a customer. Some common notations are:
The number of service channels (or servers). The M/M/1 queue has a single server and the M/M/c queue c servers.
The capacity of queue, or the maximum number of customers allowed in the queue. When the number is at this maximum, further arrivals are turned away. If this number is omitted, the capacity is assumed to be unlimited, or infinite.
Note: This is sometimes denoted c + K where K is the buffer size, the number of places in the queue above the number of servers c.
The size of calling source. The size of the population from which the customers come. A small population will significantly affect the effective arrival rate, because, as more customers are in system, there are fewer free customers available to arrive into the system.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service. Queueing theory has its origins in research by Agner Krarup Erlang, who created models to describe the system of incoming calls at the Copenhagen Telephone Exchange Company.
Explores statistical symmetries in random fields, emphasizing stationarity and homogeneity under various transformations and their practical implications.
We consider a source that collects a multiplicity of streams of updates and sends them through a network to a monitor. However, only a single update can be in the system at a time. Therefore, the transmitter always preempts the packet being served when a n ...
This paper shows for the first time that distributed computing can be both reliable and efficient in an environment that is both highly dynamic and hostile. More specifically, we show how to maintain clusters of size O(log N), each containing more than two ...
2013
,
We compare several languages for specifying Markovian population models such as queuing networks and chemical reaction networks. These languages -matrix descriptions, stochastic Petri nets, stoichiometric equations, stochastic process algebras, and guarded ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2009