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1 TRM!"#$%& ' *,-./ *!#!!%!&!3,&!$-!$./!!"#$%&'*" 4!5"# 6!#!-!&'!5$7!84//&'9&:*;83< 3!H*!!$!&'!5$! &!!F#!!!5$ *"P# Generaion The Transiion Rae Marix TRM for Exonenial Disribuion Absrac In some imes queuing rocess does no found soluion and so no reach o seady sae. If no use ransien soluion. This case haen when he queuing sysem is work for shor ime, arrival and service raes are flucuaion wih ime and service saion is work inermienly. In his research we sudy he ransien behavior for one of hase disribuions which is exonenial disribuion; he square coefficien of variaion o his disribuion is equal o one. Tha is he cusomer will comlee one hase in arrival saion and one hase in service saion. The case ha we assume i is iner arrival and service imes are exonenially disribued, single service saion, finie sysem caaciy, and infinie oulaion caaciy. Afer ha we generae differenial equaion for his sysem and we solved his equaion by using Rung- Kua order 4 mehod, and so obain on he ransien soluion and seady sae soluion.

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17 Recommendaions and Conclusions Conclusions 5. U? #C? >;#N#> 4G$!&-!$";%! /C>5!.<' --$!.$%>3$3!*. /;%, Recommendaions /&& 33!#T&& -<' 453%>*.!.8'%-4% /

18 References -Al-Hanbali.A.7 Absorbing rocesses: hase ye disribuion sochasic and oeraions research grou, universiy of wene. - Chevalier, J-Chr. Van den Schrieck May 6 Aroximaing he Performance of Call Ceners wih Queues using Loss Models. 3-Dakheel,F.I996, An Aroach For Deerming The Analyical Soluion The machine Inerferance model E k /E L /m/n College Of Educaion, Al-Musansiriayah Universiy. 4-Hermanns.H. and PieerKaoen.J. Auomaed comosiional markov chain generaion 5-John H.& Kuris D.999 Numerical Mehods Using malab 3 rd Ediion,Prenice Hall.Inc.Simon &Schuser Aviacom Comany. 6-Taha, Hamdy A.997 Oeraions Research An Inroducion,6 h ediion,prenice Hall.Inc.Simon &Schuser Aviacom Comany. 7-Winson.L.Wayle 994 Oeraions Research Alicaions and Algorihms Inernaional Thomson Publishing.

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