Queue theory and queue network models queueing theory and queueing networks model

(Learning for most of the month, hurriedly put something in the head to pour a little bit out, otherwise forget.) See other people's PPT is logical, one go, see how much I can tell how many things)

1 Queue theory

Queues are ubiquitous in life, such as queuing up for tickets, queuing for meals, waiting in line for subways and so on.   That will be such a queue abstraction, can be summed up in the 3 to: the total number of queues can be accommodated (for example, the canteen space is only so large, the longest team can only accommodate 20 people), service rate (such as the speed of the canteen aunt to play vegetables), waiting time. We can get the following relationship through mathematical formulas and common sense of life: total number of queues = Service rate multiplied by wait time.

Queue theory is applied to queuing of server processing, so the number of queued features is increased by one item

According to the Theory of Kenol (), it can be classified according to several elements of the queue

Distribution of the arrival rate/distribution of service rates/number of servers/capacity of the server (maximum number of request to be processed)/capacity of the total number waiting

Distributions typically include the following:
Momeryless, also known as Markov distribution, is the most mature of the research. It is characterized by the exponential distribution of the number of arrivals exponential distribution, while the interval of arrivals is Poisson distributed possion distribution

Dterminal a specified number of arrival rates, not necessarily distributed

General is a common type of distribution, for example, 20% of people every 10 minutes to one, the rest of every 30 minutes to one, partial representation of a certain pattern

Another thing that needs to be added is Service rules, such as regular first-come-first services, or other later services, or a certain level of VIP, like a bank, in which a particular group of people can take precedence.

2 Operating laws optional law

The law of operation is mainly based on the relationship between the parameters have been derived from the mathematical formula of the other, for the indirect calculation or inference

Force float Law

Equation Law Arrival rate = Throughput

3 Queue network model (from queue to queue network when distribution despatch is present)

First distinguish the next few key concepts

Station and server center concept, station indicates that there is no concept of routing between servers, when someone comes, assuming that there are multiple servers, then this person will be scheduled to take the idle server.

Service demand the time required for the server to complete the entire task

3.1 Single class station

Open

Close

3.2 Muti Class Station

There is a concept of routing when multiple types of request are present.

4 Markov chain Markov chain

Markov two important features are: 1 The current state 2 state transfer is of course based on a hypothesis and a premise. Assume that the next state depends only on the current state and is not related to the previous state. The premise is divided into discrete type Markov and continuous type

4.1 Discrete type Markov

is divided into the absorb type (which will end up in any state to a party and stop) and birth and death type (can be transferred to any other place after n transfers from any state)

5 using octave to achieve the corresponding mathematical calculation

First introduced package: Pkg Load queueing

Then calculate the adaptation scenarios for each formula according to the document

Queue theory and queue network models queueing theory and queueing networks model