Increasing convex ordering of queue length in bulk queues |
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| Authors: | Nanlian Cai Yaohui Zheng |
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| Affiliation: | a Department of Mathematics, Jimei University, Xiamen 361021, China
b School of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
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| Abstract: | This paper considers single-server bulk queues M(X)/G(Y)/1 and G(X)/M(Y)/1. In the former queue, service times and service capacity are dependent, while in the latter queue, inter-arriving times and arriving group size are dependent. We show that stronger dependence between those leads to shorter queue lengths in the increasing convex ordering sense. |
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| Keywords: | Bulk queue Queue length Supermodular order Increasing convex order |
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