带特殊重试时间的MM1重试排队模型的另一个特征值.pdf

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©!. 1˜! ¥Äk0‘AÏ­Áž m  M/M/1 ­ÁüèêÆ., XÚ\G˜m!̎f9ٽ, ,òT.= z¤ Banach ˜m¥Ė Cauchy ¯K. 0c ïĤJ. 1!ïÄT.Ì Žf3†ŒE²¡¥AŠ,  −(2λ+α+β )+√(α+β )2 +4λβ ´T̎fAÛ­ê 1  4 AŠ. …cµ M/M/1 ­Áüè, AŠ, AÛ­ê, i Abstract This thesis is divided into two chapters. Chapter 1 is split into two sections. In Section 1 we introduce briefly the history of queueing theory. In Section 2 we introduce supplementary variable technique, then we state the problem that we will study in this thesis. Chapter 2 consists of two sections. In Section 1, first we introduce the mathematical model of M/M/1 retrial queue with special retrial times, then we convert this model into an abstract Cauchy problem in a Banach space by introducing state space, operators and their domains, last we introduce the main results obtained by other reserchers. In Section 2, we study eigenvalue of the operator corresponding to this model in left half complex plane, and obtain −(2λ+α+β )+√(α+β )2 +4λβ that 4 is an eigenvalue of this operator with geometric multiplicity one. Keywords: M/M/1 retrial queue, eigenvalue, geometric multiplicity ii 888 ¹¹¹ ¥©Á‡ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i =©Á‡ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .