|
The erlang (symbol E〔(How Many? A Dictionary of Units of Measurement )〕) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. For example, a single cord circuit has the capacity to be used for 60 minutes in one hour. If one hundred six-minute calls are received on a group of such circuits, then assuming no other calls are placed for the rest of the hour, the total traffic in that hour will be six hundred minutes, or 10 erlangs. In 1946, the CCITT named the international unit of telephone traffic the erlang in honor of Agner Krarup Erlang. ==Traffic measurements of a telephone circuit== When used to represent carried traffic, a value (which can be a non-integer such as 43.5) followed by “erlangs” represents the average number of concurrent calls carried by the circuits (or other service-providing elements), where that average is calculated over some reasonable period of time. The period over which the average is calculated is often one hour, but shorter periods (e.g., 15 minutes) may be used where it is known that there are short spurts of demand and a traffic measurement is desired that does not mask these spurts. One erlang of carried traffic refers to a single resource being in continuous use, or two channels each being in use fifty percent of the time, and so on. For example, if an office has two telephone operators who are both busy all the time, that would represent two erlangs (2 E) of traffic; or a radio channel that is occupied for one hour continuously is said to have a load of 1 erlang. When used to describe offered traffic, a value followed by “erlangs” represents the average number of concurrent calls that would have been carried if there were an unlimited number of circuits (that is, if the call-attempts that were made when all circuits were in use had not been rejected). The relationship between offered traffic and carried traffic depends on the design of the system and user behavior. Three common models are (a) callers whose call-attempts are rejected go away and never come back, (b) callers whose call-attempts are rejected try again within a fairly short space of time, and (c) the system allows users to wait in queue until a circuit becomes available. A third measurement of traffic is instantaneous traffic, expressed as a certain number of erlangs, meaning the exact number of calls taking place at a point in time. In this case the number is an integer. Traffic-level-recording devices, such as moving-pen recorders, plot instantaneous traffic. The concepts and mathematics introduced by Agner Krarup Erlang have broad applicability beyond telephony. They apply wherever users arrive more or less at random to receive exclusive service from any one of a group of service-providing elements without prior reservation, for example, where the service-providing elements are ticket-sales windows, toilets on an airplane, or motel rooms. (Erlang’s models do not apply where the server-providing elements are shared between several concurrent users or different amounts of service are consumed by different users, for instance, on circuits carrying data traffic.) Offered traffic (in erlangs) is related to the call arrival rate, λ, and the average call-holding time (the average time of a phone call), ''h'', by: : provided that ''h'' and λ are expressed using the same units of time (seconds and calls per second, or minutes and calls per minute). The practical measurement of traffic is typically based on continuous observations over several days or weeks, during which the instantaneous traffic is recorded at regular, short intervals (such as every few seconds). These measurements are then used to calculate a single result, most commonly the busy hour traffic (in erlangs). This is the average number of concurrent calls during a given one-hour period of the day, where that period is selected to give the highest result. (This result is called the time-consistent busy hour traffic). An alternative is to calculate a busy hour traffic value separately for each day (which may correspond to slightly different times each day) and take the average of these values. This generally gives a slightly higher value than the time-consistent busy hour value. The goal of Erlang’s traffic theory is to determine exactly how many service-providing elements should be provided in order to satisfy users, without wasteful over-provisioning. To do this, a target is set for the grade of service (GoS) or quality of service (QoS). For example, in a system where there is no queuing, the GoS may be that no more than 1 call in 100 is blocked (i.e., rejected) due to all circuits being in use (a GoS of 0.01), which becomes the target probability of call blocking, ''Pb'', when using the Erlang B formula. There are several Erlang formulae, including Erlang B, Erlang C and the related Engset formula, based on different models of user behavior and system operation. These are discussed below, and may each be derived by means of a special case of continuous-time Markov processes known as a birth-death process. Where the existing busy-hour carried traffic, ''E''c, is measured on an already-overloaded system, with a significant level of blocking, it is necessary to take account of the blocked calls in estimating the busy-hour offered traffic ''E''o (which is the traffic value to be used in the Erlang formula). The offered traffic can be estimated by ''E''o = ''E''c/(1 − ''P''b). For this purpose, where the system includes a means of counting blocked calls and successful calls, ''P''b can be estimated directly from the proportion of calls that are blocked. Failing that, ''P''b can be estimated by using ''E''c in place of ''E''o in the Erlang formula and the resulting estimate of ''P''b can then be used in ''E''o = ''E''c/(1 − ''P''b) to estimate ''E''o. Another method of estimating ''E''o in an overloaded system is to measure the busy-hour call arrival rate, ''λ'' (counting successful calls and blocked calls), and the average call-holding time (for successful calls), ''h'', and then estimate ''Eo'' using the formula ''E'' = ''λh''. For a situation where the traffic to be handled is completely new traffic, the only choice is to try to model expected user behavior, estimating active user population, ''N'', expected level of use, ''U'' (number of calls/transactions per user per day), busy-hour concentration factor, ''C'' (proportion of daily activity that will fall in the busy hour), and average holding time/service time, ''h'' (expressed in minutes). A projection of busy-hour offered traffic would then be ''E''o = (NUC/60)''h'' erlangs. (The division by 60 translates the busy-hour call/transaction arrival rate into a per-minute value, to match the units in which ''h'' is expressed.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Erlang (unit)」の詳細全文を読む スポンサード リンク
|