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In the basic queuing model, service requests, such as phone calls, from traffic sources arrive at a service facility of one or more servers. The stream over time of service requests is the arrival process.
Since service facilities-TDM buses, trunk groups, and touch tone receivers-are relatively expensive, they are usually sized to grade of service (GoS) rather than to the maximum traffic possible. Grade of service is usually designated in the form "P001," which indicates that the probability of a service request finding all servers busy is 1 in 1,000 or 0.001. P01 is typical for trunk groups, P001 for port network resources, and P0001 inter port network resources.
The load associated with individual entities, such as stations or trunks, is traditionally represented in units of "Cent Call Seconds", or CCS. One CCS is 100 call seconds. The load associated with a group of entities, such as a trunk group or a TDM bus, is usually represented in Erlangs. The Erlang load is the time average number of entities busy for a given time period. The EBC calculation for the number of servers provides the GoS "buffer" required on top of the carried load in Erlangs.
Facilities are usually sized to load during the "Busy Hour". This usually means the busy hour of the year. Switching systems are usually rated by the number of busy hour calls (BHCs) they can support.
The offered load to a service facility over an interval is the mean or expected amount of time required to serve all arrivals during the interval. The carried load is the expected load the service facility will handle. The following equation usually holds:
Carried load = Offered Load x (1 - GoS).
The arrival process for telephone traffic to a switch such as a central office or PBX can typically be modeled as a Poisson Process. If the arrival process is Poisson, the time between arrivals has an exponential distribution. Queuing models with Poisson arrivals are said to be infinite source models, because the number of arrivals in service has no effect on the arrival process. Service times for arrivals are usually assumed to be exponentially distributed for telephony traffic. If blocked arrivals immediately leave and never return, the queuing model is called an "Erlang B", or EB. If blocked arrivals always queue, and there is no queue limit, the model is called an "Erlang C" or EC. In a "Retrial" queuing, a percentage of blocked arrivals retry after an exponentially distributed period which is the same as the service time. The retrial model becomes the Erlang B if the percentage of retrials is 0.
In the EB and EC models, three numbers are significant: the load (carried or offered), the GoS, and the number of servers. Any two determine the third, and tables of these relationships are widely available, as are algorithms for computer calculation. Let EB(.) and EC(.) be the functions that return the number of servers for the Erlang B and Erlang C given the carried load and the grade of service. The following always holds:
The standard retrial tables mentioned earlier give an intermediate result, but these tables were designed for PSTN traffic. For PBX users, the time between retrials is much shorter. To account for retrials in a PBX environment, use an average:
For low blocking levels, all of these results are approximately the same, so using a simple Erlang B is usually sufficient.
Another type of model is the finite source or "Engset" model. In this model, the arrival process is no longer Poisson. There are a finite number of traffic sources. Service times are exponential. The time between service completion and a new service request for a given source is exponential.
The Engset is used when the ratio of the number of sources to servers is small. To avoid using this model, check to make sure that the number of sources is not less than the number of servers provisioned using the EBC calculation. If so, size the facility to the number of sources.
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