Queuing system: definition and concept. Queuing system

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01/20/10 68K

Users of Internet resources have not yet had time to comprehend and get used to what Web 2.0 means, when two more new names arose, which are a direct result of the development of this Web 2.0.

Not many people differentiate between SMO and SMM; for most, it’s the same thing. However, the issue of dividing these concepts into different definitions is quite controversial. You can put it this way: SMO is a certain part of SMM.

The Word of Mouth Laboratory, a recognized expert on social networks, has conditionally separated these two terms for the purpose of greater understanding on the topic of achieving successful promotion in in social networks.

According to experts, SMO (Social media optimization)– this is public media optimization or optimization for social media.

  1. SMO is not a social media job. The work is carried out on a personal website. The work consists of preparing the site for the appearance of users from various social networks.
  2. SMO is the work with content posted on your website. In order to make it interesting and friendly for users from various social networks, and to make them regular visitors and encourage them to attract friends and acquaintances to the site by giving them a link to the site
  3. SMO is the transformation of your own website in order to optimally comply with the technical mechanisms used in social networks and the relevance (appropriateness) of the content located on it for all groups of users who visit the site.
  4. SMO is about creating an atmosphere of sincerity and friendliness on the site, which should be combined with colorful illustrations and video materials. All this should attract and meet a loyal audience from social networks. They can be posts High Quality, which will cause the user an irresistible desire to add the resource to his bookmarks.
  5. SMO is the user-friendliness of a site, which starts with a convenient and understandable interface and usability for anyone, and ends with friendliness in terms of permissions, selected fonts and readable content.
  6. SMO is a built infrastructure of your own website, the presence of outgoing channels and the ability to easily and quickly export content. This is necessary so that the user can easily transfer selected content to a social network, blogosphere, social bookmarks and PPC aggregators. This provides the opportunity to subscribe to the PRS on the site, add the site to bookmarks, iGoogle and Yandex feed, or simply subscribe to the e-mail newsletter. This is the presence of buttons for posting news messages and announcements automatically on social networks. This is providing the opportunity for users to create gadgets (applications) on their website and website gadgets on user blogs.
  7. SMO represents a reduction in care maximum size- this is when the user does not want to go to subsequent pages of the site and leaves the one he came to. This can be achieved by creating a vivid list of the most the best materials and announcements by placing it in the most visible place, providing the user with an easy transition through them. You can also call for this.
  8. SMO is an opportunity to open opportunities for the exchange of opinions on your website, regularly and actively supporting discussions, protecting against spam, tagging, supporting and thanking the best commentators.

According to the definition of the same experts, SMM (Social media marketing) is social media marketing or marketing in social media.

  1. SMM is not work on your own website. SMM consists of working on websites belonging to other Web 2.0 sites or specially created ones of your own, in any of the social networks, on forums and blogs, in any of the places where Internet users communicate, as well as on instant messaging services.
  2. SMM is a set of activities aimed at promoting a website, various products and services offered in any social network. And attracting interested users from social networks to the main website.
  3. SMM is intended to unobtrusively post or encourage the placement in social resources, forums and blogs of relevant topics, links to sections of its website or the website itself.
  4. SMM serves as a tool for delivering interesting information to the user about the product contained on the main site, which she is interested in, with reviews about it from other users and the indispensable support for the exchange of opinions that has arisen.
  5. SMM provides for the presence of bright, loud, provocative headlines aimed at awakening the user’s interest and desire to familiarize themselves with the material.
  6. SMM is aimed at merging and uniting with the audience. This audience does not want advertising about goods and services. She doesn't want to see a non-promoter, but she wants an expert. She needs communication! And in exchange for attention, I’m ready to listen to a series of useful tips and recommendations that are authoritative, reliable and verified.

Article based on materials: laboratories Word of mouth

This section discusses QSs that have both an input flow and a flow of served clients. Structures are being explored in which they operate in parallel from nodes (devices), so that they can simultaneously be serviced directly from clients. In this case, all servicing devices are assumed to be equivalent in terms of performance. Schematically, such a serving system is depicted in Fig. 1. Note that at any (arbitrarily selected moment) of time, all clients in the system should be divided into those who are in queue and, therefore, waiting to be served, and those who are already served.

Picture 1

The designations that are most suitable for QS with parallel “connected” devices have long been unified and have the following structure:

(a/b/c): (d/e/f),

where the symbols a, b, c, d, e and f are associated with the specific most essential elements of the model representation of queuing processes and are interpreted as follows:

a - distribution of moments of receipt of requests for service;

b- distribution of service time (or departures of served clients)

c - number of parallel operating service nodes (c=1, 2...);

d - queue discipline;

e - maximum number requirements allowed into the system (number of requests in the queue + number of requests accepted for service);

f is the capacity of the source generating service requests.

To specify a and b, the following standard notation is used:

M - Poisson distribution of the moments of receipt of requests for service or serviced clients leaving the system (or exponential distribution of time intervals between the moments of successive arrivals or durations of customer service);

D- fixed (deterministic) time interval between the moments of successive receipts of requests for service into the system or deterministic (fixed) duration of service;

Ek - Erlang distribution or gamma distribution of time intervals between the moments of successive arrivals of requests to the servicing system or service durations (where k is understood as a distribution parameter);

GI - distribution of an arbitrary type of moments of receipt of service requests into the system (or time intervals between successive receipts of requests);

G - distribution of an arbitrary type of moments of departure of serviced clients from the system (or duration of service).

To illustrate, consider the structure (M/D/10):(GD/N/). In accordance with the accepted notation, here we are talking about a QS with a Poisson input flow, a fixed service time and ten parallel operating service nodes. The queue discipline is not regulated, which is emphasized by the pair of GD symbols. In addition, no matter how many requests arrive at the input of the serving system, this system (queue + clients being served) cannot accommodate more than N requests (clients), i.e. clients who are not included in the waiting block are forced to be served elsewhere. Finally, the source generating service requests has unlimited (infinitely large) capacity.

The ultimate goal of analyzing queuing systems and processes is to develop criteria (or indicators) for the effectiveness of the QS operation. In this regard, it is important to immediately emphasize one important circumstance: since the queuing process occurs over time, we will be interested only in the stationary process.

If stationarity conditions are met, we will be interested in the following operational characteristics of the QS:

Pn is the probability that there are n clients (service requests) in the system;

Ls is the average number of clients (service requests) in the system;

Lq is the average number of clients in the queue for service;

Ws is the average duration of a client’s (service request) stay in the system;

Wq is the average duration of a client’s (service request) stay in the queue.

A-priory

There is a strict relationship between Ls and Ws (as well as between Lq and Wq), so that, knowing the numerical values ​​of one of these quantities, you can easily find the value of the other quantity. In particular, if the frequency of service requests entering the system is equal to (the intensity of requests), then we have

The above relationships are also valid under much less stringent assumptions that do not impose any special restrictions on the distribution of the moments of successive arrivals of demands, or on the distribution of service durations. However, in cases where the frequency of receipt of requests for service is equal, but not all requests have the opportunity to get into the serving system (for example, due to the insufficient capacity of the waiting block), relations (1) must be modified by such a new definition of the parameter that allows would take into account only the requirements that are actually “allowed” into the system. Then, introducing into consideration


will have

In general

This means that only a fraction of incoming service requests actually “penetrate” the system. But in any case, we can establish the dependence of the EFF on LS Lq as follows. A-priory

If average speed service equals and, therefore, the average service duration equals 1/, then the following relationship holds:

Multiplying the left and right sides of this relation by, we get

The last relation remains valid even if we replace it with EFF. In this case, for the EFF we can write

When analyzing all the models considered below, the main attention will be focused on obtaining formulas for pn, since, knowing pn, it is not difficult to determine the value of all the main operational characteristics of the queuing process of interest to us in the order indicated below:

Note that in most cases, when calculating pn values ​​within the framework of the corresponding mathematical model, no special difficulties are encountered. As for the distributions of waiting times, their numerical assessment may be far from simple. Thus, in most cases it is more convenient to calculate WS and Wq in terms of LS and Lq.

Example. Let's consider a QS with one serving device. Let the average number of requests entering the system per hour be three(), and the service rate be 8()requests per hour. The probability pn that there will be n requirements in the system is determined on the basis of data obtained as a result of observations of the functioning of the system. Let us assume that we have the following statistical estimates:

(As we see below, pn values ​​are calculated using formulas that have to be specially derived for each specific type of queuing model.)

Based on the above input data, LS, WS, Wq and Lq can be calculated. Let's start by determining the average number of requirements in the serving system:

requirements. Since =3, for the average duration of stay of a requirement in the system we have

Considering that =8, we obtain an estimate of the average length of stay in the queue

from which it follows that the average number of “clients” in the queue is equal to

Using the data given in the previous example as initial data, we calculate:

(a) Average number of queued requests, using directly known values pn.

A-priory

Substitute the corresponding values

(b) Average number of clients served by the system.

By definition, the average number of clients served by the system is LS-Lq. From the above formulas we find

As the parameter increases, LS and Lq will increase, and as the parameter increases, WS and Wq will decrease.

SMO with in English translated as social media optimization. It pursues the goal of attracting and retaining visitors on social networks. The CMO is also aimed at working to modernize the site.

CMO is internal promotion, and CMM is external.

CMO optimizes only the internal component; it does not concern website promotion on social networks.

Every promising entrepreneur strives to optimize and promote their website. But along with search engine optimization, there is also social optimization. These are SMO and SMM. Social optimization can significantly increase the attendance of the target audience. Therefore, you should not limit yourself to just promoting your website. CMO and CMM differ slightly in procedure.

If site promotion is aimed at robotic algorithms, then CMO and SMM work on audience optimization.

Components of internal optimization of a QS

With QS, all work can be done on the website without investment Money. TO internal work optimization includes technical components and site audit, work on filling and changing the site’s content, work on the appearance, linking, installation of buttons, site maps, comments from social networks, formation of blocks.

Audit includes analysis weaknesses site and their corrections. Design and optimization are being revised introductory words for ease of search, competitiveness. During a technical audit, the content is checked for literacy, link functionality, and loading speed. Also during the audit, many other parameters are checked, and all this is aimed at effective work pages.

It's no secret that the content of the site constantly needs to be updated, changed, and introduced innovations. As a rule, after developing a full-fledged website, changing the content is a continuous process. Competent and consistent articles are very important. The behavioral response of search engine systems largely depends on this.

Also plays an important role appearance site, its design. It should be beautiful, not overloaded with tacky colors, be different from competitive sites, and be correctly located. Visual perception also attracts visitors. If the appearance is beautiful and solid, then this makes a positive impression on the site owner, as it produces aesthetic pleasure. It is also very important that the information is arranged clearly and logically so that you can quickly find the information you need.

Site linking affects navigation. The site becomes more understandable for search engines and users.

It is good to install a site map that contains links to all pages. It is better to create it on a separate page. This will improve navigation and ease of use.

The site needs to provide space for comments from social networks. Registered users on social networks will be able to comment on articles and other text applications on your site. These comments are displayed on social networks, which will serve as advertising for you.

One more useful thing is the formation of blocks. On the edge of the website page you can place a column (sidebar) with fresh and interesting articles. This will attract readers as people like to stay updated. Perhaps this will be a good incentive to visit the site more than once.

P.S. If you don’t want to delve into all the details and tricks of website promotion, then we recommend entrusting this matter to professionals. Promoting a website on the Internet professional level is carried out by the company JoomStudio.com.ua. For website promotion, we recommend contacting them.

In many areas of economics, finance, production and everyday life important role play queuing systems(SMO), i.e. such systems in which, on the one hand, massive requests (demands) arise for the performance of any services, and on the other hand, these requests are satisfied.

Examples of QS in the financial and economic sphere include systems that are: banks various types, insurance organizations, tax inspectorates, auditing services, various systems communications (including telephone stations), loading and unloading complexes (commodity stations), gas stations, various enterprises and service organizations (shops, catering establishments, information desks, hairdressers, ticket offices, currency exchange offices, repair shops, hospitals).

Systems such as computer networks, systems for collecting, storing and processing information, transport systems, automated production areas, production lines can also be considered as a kind of QS.

In trade, many operations are performed in the process of moving the mass of goods from the sphere of production to the sphere of consumption. Such operations are: loading and unloading of goods, transportation, packaging, packaging, storage, display, sale, etc. Trading activities are characterized by mass receipt of goods, money, mass customer service, etc., as well as performing relevant operations that are random in nature. All this creates unevenness in work trade organizations and enterprises, creates underloads, downtime and overloads. Queues take up a lot of time, for example, for customers in stores, drivers of cars at commodity depots waiting for unloading or loading.

In this regard, problems arise in analyzing the work of, for example, the sales department, trading enterprise or sections, to evaluate their activities, identify shortcomings, reserves and ultimately take measures aimed at increasing its effectiveness. In addition, problems arise related to the creation and implementation of more economical methods of performing operations within a section, department, trading enterprise, vegetable base, trade department, etc. Consequently, in the organization of trade, the methods of queuing theory make it possible to determine the optimal number of retail outlets of a given profile, the number of sellers, the frequency of delivery of goods and other parameters.

Another typical example of queuing systems can be warehouses or bases of supply and sales organizations, and the task of queuing theory comes down to establishing the optimal ratio between the number of service requests arriving at the base and the number of servicing devices, in which the total maintenance costs and losses from transport downtime would be minimal. Queuing theory can also be used when calculating area storage facilities, while the warehouse area is considered as a service device, and the arrival of vehicles for unloading is considered as a requirement.


Main characteristics of the SMO

The QS includes the following elements: source of requirements, incoming flow of requirements, queue, serving device (service channel), outgoing flow of requirements (serviced applications).

Each QS is designed to service (fulfill) a certain flow of applications (requirements) arriving at the input of the system, generally not regularly, but at random times. Service of applications also does not last continuously, in advance known time, but a random time, which depends on many random reasons. After servicing the request, the channel is released and ready to receive the next request.

The random nature of the flow of requests and the time of their servicing leads to an uneven load on the QS: at some time intervals, unserved requests may accumulate at the input of the QS, which leads to an overload of the QS; at some other time intervals, when there are free channels at the input of the QS, there are no requests will be, which leads to underloading of the QS, i.e. to the idleness of its channels. Applications accumulating at the entrance of the QS either “join” the queue, or for some reason the impossibility of further stay in the queue leaves the QS unserved.

The QS diagram is shown in Figure 5.1.

Figure 5.1 - Scheme of the queuing system

Each QS includes in its structure a certain number of servicing devices, which are called service channels. The role of channels can be played by various devices, persons performing certain operations (cashiers, operators, salespeople), communication lines, cars, etc.

Each QS, depending on its parameters: the nature of the flow of applications, the number of service channels and their productivity, as well as the rules for organizing work, has a certain operating efficiency (throughput), allowing it to more or less successfully cope with the flow of applications.

QS is the subject of study queuing theory.

Purpose of Queuing Theory— development of recommendations for the rational construction of the QS, the rational organization of their work and regulation of the flow of applications to ensure high efficiency of the functioning of the QS.

To achieve this goal, the tasks of queuing theory are set, which consist in establishing the dependencies of the effectiveness of the functioning of the QS on its organization (parameters).

As performance characteristics of the QS system You can choose three main groups of (usually average) indicators:

1. Indicators of effectiveness of using QS:

1.1. Absolute throughput QS is the average number of requests that the QS can serve per unit of time.

1.2. Relative capacity of the QS is the ratio of the average number of applications served by the QS per unit of time to the average number of received applications during the same time.

1.3. Average duration of the employment period of the CMO.

1.4. QS utilization rate is the average share of time during which the QS is busy servicing requests.

2. Application service quality indicators:

2.1. Average waiting time for an application in the queue.

2.2. Average time an application stays in the CMO.

2.3. The probability of a request being denied service without waiting.

2.4. The probability that an received application will be immediately accepted for service.

2.5. Law of distribution of waiting time for an application in a queue.

2.6. The law of distribution of the time an application stays in the QS.

2.7. The average number of applications in the queue.

2.8. Average number of applications in the CMO, etc.

3. Indicators of the effectiveness of the pair "CMO - consumer", where “consumer” is understood as the entire set of applications or some of their sources (for example, the average income brought by the QS per unit of time, etc.).

The random nature of the flow of applications and the duration of their service gives rise to random process . Because moments in time T i and time intervals for receipt of applications T, duration of maintenance operations T obs, standing in line T very good, queue length l very goodrandom variables, then the characteristics of the state of queuing systems are probabilistic in nature. Therefore, to solve the problems of queuing theory, it is necessary to study this random process, i.e. build and analyze its mathematical model.

The mathematical study of the functioning of a QS is significantly simplified if the random process occurring in it is Markovian. For a random process to be Markovian, it is necessary and sufficient that all flows of events under the influence of which transitions of the system from state to state occur are (the simplest) Poisson.

The simplest flow has three basic properties: ordinary, stationary and lack of aftereffect.

Ordinary flow means the practical impossibility of simultaneous receipt of 2 or more demands. For example, the probability that several cash registers in a self-service store will fail at the same time is quite small.

Stationary is a flow for which the mathematical expectation of the number of demands entering the system per unit of time (we denote λ ), does not change over time. Thus, the probability of a certain number of demands entering the system during a given period of time ?T depends on its magnitude and does not depend on the origin of its counting on the time axis.

No aftereffect means that the number of requirements received by the system before the moment T, does not determine how many requests will enter the system over time (T+?T). For example, if in cash register At the moment there was a break in the cash register tape and it was repaired by the cashier, this does not affect the possibility of a new break at this cash register at the next moment, and even more so on the likelihood of a break occurring at other cash registers.

For the simplest flow, the frequency of requests entering the system obeys Poisson’s law, i.e., the probability of arrival in time T smooth k requirements is given by the formula

, (5.1)

Where λ intensity of applications flow, i.e. the average number of applications received by the QS per unit of time,

, (5.2)

Where τ — the average value of the time interval between two adjacent applications.

For such a flow of applications, the time between two neighboring applications is distributed exponentially with a probability density

The random waiting time in the queue for the start of service can also be considered distributed exponentially:

, (5.4)

Where ν queue traffic intensity, i.e. the average number of applications arriving for service per unit of time,

Where T och- average value of waiting time in queue.

The output flow of requests is associated with the service flow in the channel, where the service duration T obs is a random variable and in many cases obeys the exponential distribution law with density

, (5.6)

Where μ service flow intensity, i.e. the average number of applications served per unit of time,

. (5.7)

An important characteristic of a QS system that combines indicators λ And μ , is load intensity, which shows the degree of coordination of the specified flows of applications:

Listed indicators k, τ, λ, l och, T och, ν, T obs, μ, ρ, Р k are the most common for QS.

Queuing system(SMO) is a system that services incoming requests. Requirements in the QS are serviced by servicing devices. A classical QS contains from one to an infinite number of devices. Depending on the availability of the ability to wait for incoming requirements to begin servicing, the QS is divided into

  1. systems with losses, in which requests that do not find a single free device at the time of arrival are lost;
  2. systems with waiting, in which there is an infinite capacity drive to buffer incoming requests, while the waiting requests form a queue;
  3. systems with a storage device of finite capacity (waiting and restrictions), in which the queue length cannot exceed the storage capacity; in this case, a demand arriving at an overcrowded QS (there are no free places to wait), is lost.

A requirement is selected from the queue for servicing using the so-called servicing discipline. Examples of these are FCFS/FIFO (first in first out), LCFS/LIFO (last in first out), random. In wait systems, the storage device can generally have a complex structure.

Basic concepts of QS

Requirement(application) - request for service.

Incoming Requirements Flow- a set of requirements received by the QS.

Service time- the period of time during which the request is serviced.

Mathematical model of QS is a set of mathematical expressions that describe the incoming flow of requirements, the service process and their relationship.

see also

Literature

  • Kleinrock L. Queuing theory. - M.: Mechanical Engineering, 1979. - P. 432.
  • Bocharov P.P., Pechinkin A.V. Queuing theory. - M.: RUDN, 1995. - P. 530.
  • Hemdi A. Taha Chapter 17. Queuing systems // Introduction to Operations Research = Operations Research: An Introduction. - 7th ed. - M.: “Williams”, 2007. - pp. 629-697. - ISBN 0-13-032374-8

Wikimedia Foundation. 2010.

  • Halle, Emil
  • Oscar (film award, 1979)

See what a “Queuing system” is in other dictionaries:

    queuing system - SMO System, designed to serve random flows of subscriber calls in communication networks (Fig. Q 3). Generally accepted symbol, used to describe queuing systems, consists of three symbols A/S/m, where the symbol A... ...

    Queuing system- a set of points (channels, stations, devices) to which, at random or non-random moments in time, service requests (requirements) are received that must be satisfied. There are many examples of such systems...

    QUEUING SYSTEM - mathematical model, created to study the quality of operation of real systems in which sequences of homogeneous elementary maintenance operations are implemented. S.m.o. – the main subject of research in the theory of queuing. S.m.o.... ... Large economic dictionary

    Multiphase queuing system- a system in which an received request goes through several stages of processing sequentially. To analyze such systems, it is necessary to know not only the length of the queue, the waiting time for service, the load of each... ... Economic and mathematical dictionary

    multiphase queuing system- A system in which an received request goes through several stages of processing in succession. To analyze such systems, it is necessary to know not only the length of the queue, the waiting time for service, the load of each sequential link of the system, but also... ... Technical Translator's Guide

    Multi-channel queuing system- a system in which an incoming request can be serviced by one of several channels included in the service unit... Economic and mathematical dictionary

    multi-channel queuing system- A system in which an incoming request can be serviced by one of several channels included in the service unit. Topics: economics EN multichannel system… Technical Translator's Guide

    With a waiting multi-channel queuing system, the algorithm provides for the accumulation of calls in a queue if the system is busy at the time of their arrival; At the same time, calls are serviced in several channels simultaneously... Mathematical Encyclopedia

    QUEUING SYSTEM- with failures of the queuing system, the algorithm provides for the elimination of calls; at the time of arrival, all channels were busy. For basic definitions and notations, see Art. Queuing system. 1) Natural… … Mathematical Encyclopedia

    QUEUING SYSTEM- with a waiting and one service channel queuing system, the algorithm provides that calls that are not immediately accepted for service (caught the system busy) accumulate in a queue; while servicing the following... ... Mathematical Encyclopedia

Books

  • Queuing theory, G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko. This manual sets out in a form accessible for initial study the elements of the main directions of queuing theory - a section of probability theory that studies systems...

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