Asian Journal of Mathematics & Statistics1994-54182077-2068orgz10.3923/ajms.2011.161.167El GenidyMohammed Mohammed3201143There is always a problem in estimation of the appropriate time, for the system to make it stable and if the study time of the queue system Outside the appropriate time period that will lead the system to instability and the occurrence of losses by the maximum this time .The queue system has contains the maximum length of a queue and in this study were obtained within the time appropriate some of the data input and system-specific, where the distribution of inter-arrival time follows the standard normal distribution.]]>Luczak, M.J. and C. McDiarmid,2006Koole, G., M. Nuyens and R. Righter,2005Sadowsky, J.S. and W. Szpankowski,1992Tadj, L. and A. Hamdi,2001Nuyens, M.F.M.,2004Artalejo, J.R., A. Economou and M.J. Lopez-Herrero,2007