џWPCL ћџ2BJ|xа АH аа АА X агга ХА6p&А6p&Х аеЮ† а Hр аааУ Уб cмˆ4 PŽТ б Fascicle II.3 Р-Р Rec. E.550 Ф ФPAGE1У Уб cмˆ4 PŽТ б ЮееЃ† а HH аааб cмˆ4 PŽТ бPAGE8У Уб cмˆ4 PŽТ б Fascicle II.3 Р-Р Rec. E.550 Ѓеа H№ ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаа X  аб cмˆ4 PŽТ бAll drawings appearing in this Recommendation have been done in Autocad. ‚У УRecommendation E.550 аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаСр(:Сб cмˆ4 PŽТ бGRADEР-РOFР-РSERVICE AND NEW PERFORMANCE CRITERIA UNDER FAILURE Ср(@СCONDITIONS IN INTERNATIONAL TELEPHONE EXCHANGES аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ б1ТX ТIntroductionФ ФЦЦ а H а1.1С  СThis Recommendation is confined to failures in a single exchange and their impact on calls within that exchange Р-Р network impacts are not covered in these Recommendations. а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬа1.2С   СThis Recommendation from the viewpoint of exchange Grade of Service (GOS)йC€ Grade of Service (GOS)б cмˆ4 PŽТ бCй has been established. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬа1.3С  СIn conformity with Recommendation E.543 for transit exchanges under normal operation, this Recommendation applies primarily to international digital exchanges. However, Administrations may consider these Recommendations for their national networks. 1.4С  СThe GOS seen by a subscriber (blocking and/or delay in establishing calls) is not only affected by the variations in traffic loads but also by the partial or complete faults of network components. The concept of customerР-Рperceived GOS is not restricted to specific fault and restoration conditions. For example, the customer is usually not aware of the fact that a network problem has occurred, and he is unable to distinguish a failure condition from a number of other conditions such as peak traffic demands or equipment shortages due to routine maintenance activity. It is therefore necessary that suitable performance criteria and GOS objectives for international telephone exchanges be formulated that take account of the impact of partial and total failures of the exchange. Further, appropriate definitions, models and measurement and calculation methods need to be developed as part of this activity. 1.5С  СFrom the subscriber's point of view, the GOS should not only be defined by the level of unsatisfactory service but also by the duration of the intervals in which the GOS is unsatisfactory and by the frequency with which it occurs. Thus, in its most general form the performance criteria should take into account such factors as: intensity of failures and duration of resulting faults, traffic demand at time of failures, number of subscribers affected by the failures and the distortions in traffic patterns caused by the failures. С СHowever, from a practical viewpoint, it will be desirable to start with simpler criteria that could be gradually developed to account for all the factors mentioned above. 1.6С  СTotal or partial failures within the international part of the network have a much more severe effect than similar failures in the national networks because the failed components in the national networks can be isolated and affected traffic can be rerouted. С СFailures in the international part of the network may therefore lead to degraded service in terms of increased blocking delays and even complete denial of service for some time. The purpose of this Recommendation is to set some service objectives for international exchanges so that the subscribers demanding international connections are assured a certain level of service. С СIt should be noted however that where there are multiР-Рgateway exchanges providing access to and from a country, with diversity of circuits and provision for restoration, the actual GOS will be better than that for the single exchange. ‚У У2ТX ТGeneral considerationsФ ФЦЦ а H а2.1С  СThe new performance criteria being sought involve concepts from the field of Р"РavailabilityР"Р (intensity of failures and duration of faults) and Р"Рtraffic congestionР"Р (levels of blocking and/or delay). It is therefore necessary that the terminology, definitions and models considered should be consistent with the appropriate CCITT Recommendations on terminology and vocabulary. а H а2.2С  СDuring periods of heavy congestion, caused either by traffic peaks or due to malfunction in the exchange, a significant increase in repeated attempts is likely to occur. Further, it is expected that due to accumulated demands during a period of complete faults, the exchange will experience a heavy traffic load immediately after a failure condition has been removed and service restored. The potential effects of these phenomena on the proposed GOS under failure conditions should be taken into account (for further study). аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У3С  Сб cмˆ4 PŽТ бExchange performance characteristics under faultб cмˆ4 PŽТ бФ Ф situationsУ Уб cмˆ4 PŽТ бЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ Ф3.1С  СThe exchange is considered to be in a fault situation if any failure in the exchange (hardware, software, human errors) reduces its throughput when it is needed to handle traffic. The following four classes of exchange faults are included in this Recommendation: Та ТТ№ ТС€ Сa)СpСcomplete exchange faults;ЦЦ а H аТа ТТ№ ТС€ Сb)СpСpartial faults resulting in capacity reduction in all traffic flows to the same extent;ЦЦ а H аТа ТТ№ ТС€ Сc)СpСpartial faults in which traffic flows to or from a particular point are restricted or totally isolated from their intended route;ЦЦ а Hр аТа ТТ№ ТС€ Сd)СpСintermittent fault affecting a certain proportion of calls.ЦЦ а H а3.2С  СTo the extent practical, an exchange should be designed so that the failure of a unit (or units) within the exchange should have as little as possible adverse affect on its throughput. In addition, the exchange should be able to take measures within itself to lessen the impact of any overload resulting from failure of any of its units. Units within an exchange whose failure reduces the exchange throughput by greater amounts than other units should have proportionally higher availability (Recommendation Q.504, РSР 4). 3.3С  СWhen a failure reduces exchange throughput and congestion occurs, the exchange should be able to initiate congestion control indications to other exchanges and network management systems so as to help control the offered load to the exchange, (Recommendations E.410 and Q.506). аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У4С  Сб cмˆ4 PŽТ бGOS and applicable modelsЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ Ф4.1С  СIn this section, the terms Р"РaccessibleР"Р and Р"РinaccessibleР"Р are used in the sense defined in Recommendation G.106 (УУRed BookФФ). The GOS for exchanges under failure conditions can be formulated at the following two conceptual levels from a subscriber's viewpoint: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС4.1.1С јСб cмˆ4 PŽТ бУУInstantaneous service accessibility (inaccessibility)ЦЦ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФФС СAt this level, one focuses on the probability that the service is accessible (not accessible) to the subscriber at the instant he places a demand. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС4.1.2С јСб cмˆ4 PŽТ бУУMean service accessibility (inaccessibility)ЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФФС СAt this level, one extends the concept of Р"РdowntimeР"Р used in availability specifications for exchanges to include the effects of partial failures and traffic overloads over a long period of time. 4.2С  СBased on the GOS concept outlined in РSР 4.1, the GOS parameters for exchanges under failure conditions are defined as follows: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬа4.2.1С јСУ Уб cмˆ4 PŽТ бinstantaneous exchange inaccessibility Ф Фis the probability that the exchange in question cannot perform the required function (i.e. cannot successfully process calls) under stated conditions at the time a request for service is placed. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬа4.2.2С СУ Уmean exchange service inaccessibilityФ Ф is the average of instantaneous exchange service inaccessibility over a prespecified observation period (e.g. one year). 4.2.3С СУУNote 1ФФ Р-Р The GOS model in the case of instantaneous exchange inaccessibility parallels the concept of the call congestion in traffic theory and needs to be extended to include the call congestion caused by exchange failures classified in РSР 3.1. The GOS value can then be assigned on a basis similar to Recommendation E.543 for transit exchanges under normal operation. С СУУNote 2ФФ Р-Р A model for estimating the mean exchange inaccessibility is provided in Annex A. Though the model provides a simple and hence attractive approach, some practical issues related to measurement and monitoring and the potential effects of network management controls and scheduled maintenanceд k+д on the GOS need further study. 4.3С  СThe model in Figure 1/E.550 outlines the change in the nature of traffic offered under failure conditions. ‚Ср KСб cмˆ4 PŽТ бFigure 1/E.550 Љ T0200870Љ87 б cмˆ4 PŽТ б а H аС СIn normal conditions the congestion factorУУ BФФ is low and there should be few repeat attempts: as a consequence the trafficУУ AУУtФФФФ approximatesУУ AУУoФФФФ. С СUnder failure conditions there is a reduction in resources and the congestion factorУУ BФФ increases. This provokes the phenomenon of repeat attempts and hence the loadУУ AУУtФФФФ on the exchange becomes greater than the original УУAУУoФФФФ. а H аС СTherefore it is necessary to evaluate the congestion with the new loadУУ AУУtФФФФ assuming system stability exists, which may not always be the case. С СRecommendation E.501 furnishes the appropriate models to detect the traffic offered from the carried traffic taking into account the repeat attempts. 4.4С  СThe impact on the GOS for each of the exchange fault modes can be characterized by: Та ТР-РТ№ Тload in Erlangs (УУAУУtФФФФ) and busy hour call attempts (BHCA);ЦЦ а Hh аТа ТР-РТ№ Тinaccessibility (instantaneous and mean), congestion and delay parameters (call setР-Рup, throughР-Рconnection, etc.);ЦЦ Та ТР-РТ№ Тfault duration;ЦЦ Та ТР-РТ№ Тfailure intensity.ЦЦ а HH ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У5С  Сб cмˆ4 PŽТ бGOS standards and inaccessibilityЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ Ф5.1С  СExchange fault situations can create similar effects to overload traffic conditions applied to an exchange under fault free conditions. а H аС СIn general, digital exchanges operating in the network should be capable of taking action to ensure maximum throughput when they encounter an overload condition, including any that have been caused by a fault condition within the exchange. С СCalls that have been accepted for processing by the exchange should continue to be processed as expeditiously as possible, consistent with the overload protection strategies recommended in РSР 3 of Recommendation Q.543. 5.2С  СOne of the actions the exchange may take to preserve call processing capacity is to initiate congestion controls and/or other network management actions, to control the load offered to the exchange (Recommandations E.410, E.413 and Q.506). The most obvious impact from the caller's viewpoint may be а H аa lowering of the probability that the network as a whole will be able to complete some portion of the call attempts that the exchange is unable to accept during the failure condition. а H а5.3С  СInternational exchanges occupy a prominent place in the network and it is important that their processing capacity have high availability. There are likely to be many variations in exchange architectures and sizes that will have different impacts in the categories of failure and the resulting loss of capacity. а H аС СIn general, failures that cause large proportions of exchange capacity to be lost must have a low probability of occurring and a short downtime. It is important that maintenance procedures to achieve appropriate exchange availability performance be adopted. 5.4С  СThe formal expression of the criterion of mean exchange service inaccessibility is as follows: Let: а H аТа ТТ№ ТС€ СУУyФФ(УУtФФ):Си СIntensity of call attempts gaining access through the exchange assuming no failures.ЦЦ а H аТа ТТ№ ТС€ СУУsФФ(УУtФФ):Си СIntensity of call attempts actually given access through the exchange, taking into account the fault conditions which occur in the exchange.ЦЦ а H аThen the mean exchange service inaccessibility during a period of timeУУ TФФ is given by аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СPƒФФ = eq \f( 1,УУ TФФ) \i(0,УУT,ФФ )УУ ФФeq \f(УУ yФФ(УУtФФ) Р-РУУ sФФ(УУtФФ),УУ yФФ(УУtФФ))УУ dtФФ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СAnnex A describes a practical implementation of this criterion. а H аС СFor periods in which the exchange experiences a complete fault, i.e.УУ sФФ(УУtФФ) = 0, the expression: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8Сeq \f(ƒУУyФФ(УУtФФ) Р-РУУ sФФ(УУtФФ),УУ yФФ(УУtФФ)) is equal to 1. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СThe contribution of such periods to the total criterionУУ PФФ may then be expressed simply as the fractionУУ PУУб cмˆ4 PŽТ бtotalб cмˆ4 PŽТ бФФФФ of the evaluation periodУУ TФФ during which complete exchange outage due to failure occurred. а H аС СThe objective forУУ PУУб cмˆ4 PŽТ бtotalб cмˆ4 PŽТ бФФФФ is given asУУ PУУб cмˆ4 PŽТ бtotalб cмˆ4 PŽТ бФФФФ not more than 0.4 hours per year. а H аС СFor the period of partial failure, it is convenient to also express the objective as equivalent hours per year Р-Р the term equivalent is used because the duration of partial faults is weighted by the fraction: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8Сeq \f(ƒУУyФФ(УУtФФ) Р-РУУ sФФ(УУtФФ),УУ yФФ(УУtФФ)) а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаof call attempts denied access. The objectives for the contribution of period of partial exchange faults to the total criterionУУ PФФ is given by: С СУУPУУб cмˆ4 PŽТ бpartialб cмˆ4 PŽТ бФФФФ not more than 1.0 equivalent hours per year. С СNote that by definitionУУ PФФ =УУ PУУб cмˆ4 PŽТ бtotalб cмˆ4 PŽТ бФФФФ +УУ PУУб cмˆ4 PŽТ бpartialб cмˆ4 PŽТ бФФФФ С СThe inaccessibility criterion does not cover: Та ТР-РТ№ Тplanned outagesЦЦ Та ТР-РТ№ Тfaults with duration of less than 10 secondsЦЦ Та ТР-РТ№ Тaccidental damage to equipment during maintenanceЦЦ Та ТР-РТ№ Тexternal failures such as power failures, etc.ЦЦ а H аС СIt does cover failures resulting from both hardware and software faults. а H аС СIn addition, the objectives relate to the exchange under normal operating conditions and do not include failures just after cutover of an exchange or those during the end of the period it is in service, i.e. the well known Р"Рbath tubР"Р distribution. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У6С  Сб cмˆ4 PŽТ бPerformance monitoringЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ ФС СCertain failure conditions [i.e. the type mentioned in РSР 3.1, b)] usually will be reflected in the normal GOS performance measurements called for in Recommendation E.543. а H аС СOther failure conditions [i.e. the type mentioned in РSР 3.1, c)] can result in a reduced performance for a portion of traffic flows but with little or no impact on measured exchange GOS. For example if a trunk module in a digital exchange fails, the traffic normally associated with that module is completely blocked, but since the attempts are also not measured the failure does not change the monitoring of the exchange GOS. С СFor this second situation, the mean inaccessibility can be calculated using direct measurement of unit outages to provideУУ mУУiФФФФ andУУ tУУiФФФФ information and estimates ofУУ bУУiФФФФ together with the model of Annex A. (See Annex A for an explanation of these symbols.) а H аС СThe estimates ofУУ bУУiФФФФ can incorporate both fixed factors based on exchange architecture and variable factors based on traffic measurements just prior to the time of failure. ‚Ср VСб cмˆ4 PŽТ бANNEX A Ср MСб cмˆ4 PŽТ б(to Recommendation E.550) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаСр EСУ УA model forб cмˆ4 PŽТ б mean exchange inaccessibility а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ ФA.1С  СLetУУ PФФ be the probability that a call attempt is not processed due to a fault in the exchange, then: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8Сeq P = \i\su(i=1,N, )ƒУУpУУiФФ bУУiФФФФСH8А"FС(AƒР-Р1) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаwhere: а H аТа ТТ№ ТС€ СУУpУУiФФФФСpСis the probability of fault modeУУ iФФ. Each fault mode denotes a specific combination of faulty exchange componentsЦЦ Та ТТ№ ТС€ СУУNФФСpСis the number of the fault modeЦЦ а H аТа ТТ№ ТС€ СУУbУУiФФФФСpСis the average proportion of traffic which cannot be processed due to the fault modeУУ iФФ. It is a function of the specific fault present and the offered traffic load at the time of the failure condition.ЦЦ а H аС СDuring a period of timeУУ TФФ, the fault probabilityУУ pУУiФФФФ may be estimated by: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СpƒУУiФФФФ = eq \f(УУ mУУiФФФФ .УУ tУУiФФФФ,УУ TФФ) УУiФФ = 1, 2, . . .УУ NФФ СHBА"FС(AƒР-Р2) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаwhere: а H аТа ТТ№ ТС€ СУУmУУiФФФФСpСis the number of occurrences of fault modeУУ iФФ during the periodУУ TФФЦЦ Та ТТ№ ТС€ СУУtУУiФФФФСpСis the average duration of occurrences of fault modeУУ iФФЦЦ а H аС СAs a practical matter, one may wish to exclude from the calculation faults of duration less than 15 seconds. а H аС СУУNote 1ФФ Р-Р A given fault mode causes the exchange to enter the correspondingд Д-д fault state, which is characterized by a given mean duration and a functionУУ bУУiФФФФ giving the proportion of offered traffic affected. In principle, the possible number of fault modes can be very large because of the number of combinations which can occur. In practice this number can be reduced by considering all fault modes with the sameУУ bУУiФФФФ andУУ tУУiФФФФ as equivalent. а H аС СУУNote 2ФФ Р-Р УУbУУiФФФФ should take into account the distribution of traffic during a day and the probability of fault modeУУ iФФ occurring in a given time period. The value assigned in the above model should be the averageУУ bУУiФФФФ value for all hours considered in these distributions. For example, a partial fault affecting 20% of the exchange traffic throughput in the busy hour and 2 similar hours, could be evaluated to effect a 10% reduction in 4 other moderately busy hours and to have negligible impact during all other hours. If this fault is considered to be equally probable in time, the average value ofУУ bУУiФФФФ can be obtained as follows: а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СbƒУУiФФФФ = Sum ofeq \b\bc\( (\f( Percentage of traffic affected РxР number of relevant busy hours, 24 hours)) = а H аС СС pССШ8С=eq \f( 0.2 ƒРxР 3, 24) +eq \f( 0.1 РxР 4, 24) +eq \f( 0.0 РxР 17, 24) = 0.025 + 0.0167 = 0.0417 а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СУУNote 3ФФ Р-Р The probability that a call attempt is not processed relates to the category of traffic affected by the fault. Other traffic will experience a different GOS depending on system architecture which is not taken into account in this Recommendation. For example, partial faults which remove from service blocks of trunks connected to an exchange have the effect of reducing the total traffic offered to the exchange. The traffic flows not using the failed trunks could thus have a slightly improved GOS. A.2Тh  ТУУExample for calculating the inaccessibility, PЦЦ ФФС СSee Table AР-Р1/E.550. ‚Ср RСб cмˆ4 PŽТ бTABLE A.1/E.550 Ср 8СУ УAn example of using the model for calculating the inaccessibility PФ Ф Ср MС(УУTФФ = 1 year = 8760 hours) б cмˆ4 PŽТ бвЦ„HP @ H8@08"Цв‡аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P P џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаСр XСааб cмˆ4 PŽТ бУУbб cмˆ4 PŽТ бУУiФФб cмˆ4 PŽТ б Ср XСmУУб cмˆ4 PŽТ бiФФб cмˆ4 PŽТ б Ср XСtб cмˆ4 PŽТ бУУiб cмˆ4 PŽТ бФФ Ср VСpУУб cмˆ4 PŽТ бiФФб cмˆ4 PŽТ б . bб cмˆ4 PŽТ бУУiФФб cмˆ4 PŽТ б а 08 ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџpи P P 0џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бˆа 08 аФФб cмˆ4 PŽТ бвЦ„HP @ H8@08"Цв‡а 0р аб cмˆ4 PŽТ бAverage proportion of traffic which cannot be processed Number of failures of Ср:рСtype i per year Average duration of failure type i (hours) Probability that a call attempt is not processed (РxР 10УУб cмˆ4 PŽТ бР-Р5ФФб cмˆ4 PŽТ б) а 08 аб cмˆ4 PŽТ бˆа 08 аб cмˆ4 PŽТ бвЦ„HP @ H8@08"Цв‡Ср:xСб cмˆ4 PŽТ б1.00 Ср:xƒС2 Ср:x‚С0.2 Ср:xС4.56 а 08 аб cмˆ4 PŽТ бˆа 08 аб cмˆ4 PŽТ бвЦ„HP @ H8@08"Цв‡Ср:xСб cмˆ4 PŽТ б0.40 Ср:xƒС3 Ср:xС0.22 Ср:xС3.01 а 08 аб cмˆ4 PŽТ бˆа 08 аб cмˆ4 PŽТ бвЦ„HP @ H8@08"Цв‡Ср:xСб cмˆ4 PŽТ б0.20 Ср:xƒС4 Ср:x‚С0.3 Ср:xС2.74 а 08 аб cмˆ4 PŽТ бˆа 08 аб cмˆ4 PŽТ бвЦ„HP @ H8@08"Цв‡Ср:xСб cмˆ4 PŽТ б0.10 Ср:xƒС6 Ср:x‚С0.4 Ср:xС2.74 а 08 аб cмˆ4 PŽТ бˆа 08 аб cмˆ4 PŽТ бвЦ„HP @ H8@08"Цв‡Ср:xСб cмˆ4 PŽТ б0.05 Ср:x‚С10 Ср:x‚С0.5 Ср:xС2.85 а 08 аб cмˆ4 PŽТ бˆа Hh ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СThe value ofУУ PФФ is the sum of the individualУУ pУУiФФФФ.УУbУУiФФФФ terms in Table AР-Р1/E.550. In this exampleУУ PФФ = 15.90 РxР 10УУб cмˆ4 PŽТ бР-Р5ФФб cмˆ4 PŽТ б which is equivalent to 1.39 hours of inaccessibility per year (1.39 = 15.90 РxР 10УУб cмˆ4 PŽТ бР-Р5ФФб cмˆ4 PŽТ б РxР 8760).УУ PФФ decomposes as follows: Та ТТ№ ТС€ СУУPб cмˆ4 PŽТ бУУtotalФФ ФФб cмˆ4 PŽТ б = 0.40 hours per year (4.56 РxР 10УУб cмˆ4 PŽТ бР-Р5ФФб cмˆ4 PŽТ б РxР 8760)ЦЦ Та ТТ№ ТС€ СУУPУУб cмˆ4 PŽТ бpartialб cмˆ4 PŽТ бФФФФ = 0.99 hours per year (the remaining part ofУУ PФФ)ЦЦ а H аA.3С  СAs a further example consider a circuit group where exchange failures may occur which disable one or more circuits (see Figure AР-Р1/E.550). It is possible to expand the formula (AР-Р1). ‚Ср JСб cмˆ4 PŽТ бFigure AР-Р1/E.550 Љ T0200880Љ87 б cмˆ4 PŽТ б а H аС СThe average proportion of trafficУУ bФФ(УУnФФ,УУ kФФ,УУ AФФ), which cannot be processed due to failures on circuits is now a function of: Та ТР-РТ№ ТУУnФФ, the size of the circuit group;ЦЦ Та ТР-РТ№ ТУУkФФ, number of circuits out of order because of the failure;ЦЦ а H аТа ТР-РТ№ ТУУAФФ, the mean traffic offered to the circuit group, in the absence of faults.ЦЦ а H аLet the throughput of a circuit group of sizeУУ nФФ with a traffic offeredУУ AФФ beУУ CУУnФФФФ(УУAФФ) Р-Р then the throughput of the same circuit group isУУ CУУnР-РkФФФФ(УУAФФ) whereУУ kФФ circuits are out of order Р-Р hence the average proportion of trafficУУ bФФ(УУnФФ,УУ kФФ,УУ AФФ) which cannot be processed because of the failure is given by: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СbƒФФ(УУn, k, AФФ) = eq \f( [УУCУУnФФФФ(УУAФФ) Р-РУУ CУУб cмˆ4 PŽТ бnР-РkФФФФб cмˆ4 PŽТ б (УУAФФ)],УУ CУУnФФФФ(УУAФФ)) СHDА"FС(AƒР-Р3) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаLet а H аС СУУfФФ(УУkФФ,УУ AФФ) be the probability for havingУУ kФФ circuits in a fault condition and the mean offered trafficУУ AФФ. The probability,УУ PУУnФФФФ, that a call attempt is not processed due to a failure on a circuit group of sizeУУ nФФ, is given by: а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СPƒУУnФФФФ = УУeq \i\su(k\l(,)A, , ) fФФ (УУk, AФФ) .УУ bФФ(УУn, k, AФФ) УУ kФФ = 1, 2, . . .УУ nФФ С  С(AР-Р4) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СIfУУ kФФ andУУ AФФ are independent then аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СfƒФФ (УУk, AФФ) =УУ fФФУУ1ФФ(УУkФФ) .УУ fФФУУ2ФФ(УУAФФ) СH7А"FС(AƒР-Р5) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаwhereУУ fФФУУ1ФФ (УУkФФ) may satisfy a binomial distribution andУУ fФФУУ2ФФ(УУAФФ) a Poisson distribution. а H аС СSuppose the traffic follows an Erlang distribution,УУ CУУnФФФФ(УУAФФ) is proportional toУУ AФФ . (1 Р-РУУ EУУnФФФФ(УУAФФ)), whereУУ EУУnФФФФ(УУAФФ) is the blocking probability expressed by the Erlang loss formula. Hence: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СbƒФФ (УУn, k, AФФ) = eq \f(УУ EУУб cмˆ4 PŽТ бnР-РkФФФФб cмˆ4 PŽТ б (УУAФФ) Р-РУУ EУУб cмˆ4 PŽТ бnб cмˆ4 PŽТ бФФФФ (УУAФФ), 1 Р-РУУ EУУб cмˆ4 PŽТ бnб cмˆ4 PŽТ бФФФФ (УУAФФ)) СHHА"FС(AƒР-Р6) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаcan be found by using the Erlang tables and then inserting the value into equation (AР-Р4).