On the stability of a partially accessible multi‐station queue with state‐dependent routing

被引:0
作者
Serguei Foss
Natalia Chernova
机构
[1] Institute of Mathematics,
[2] Novosibirsk State University,undefined
来源
Queueing Systems | 1998年 / 29卷
关键词
multi‐server queue; customer class; state‐dependent routing; stability; Markov chain; fluid limit;
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学科分类号
摘要
We consider a multi‐station queue with a multi‐class input process when any station is available for the service of only some (not all) customer classes. Upon arrival, any customer may choose one of its accessible stations according to some state‐dependent policy. We obtain simple stability criteria for this model in two particular cases when service rates are either station‐ or class‐independent. Then, we study a two‐station queue under general assumptions on service rates. Our proofs are based on the fluid approximation approach.
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页码:55 / 73
页数:18
相关论文
共 18 条
[1]  
Chen H.(1991)Discrete flow networks: bottleneck analysis and fluid approximations Math. Oper. Res. 16 408-446
[2]  
Mandelbaum A.(1995)Fluid approximations and stability of multiclass queueing networks I: work-conserving disciplines Ann. Appl. Probab. 5 637-665
[3]  
Chen H.(1995)On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid models Ann. Appl. Probab. 5 49-77
[4]  
Dai J.G.(1996)A fluid-limit model criterion for instability of multiclass queueing networks Ann. Appl. Probab. 6 751-757
[5]  
Dai J.G.(1995)Stability and convergence of moments for multiclass queueing networks via fluid limit models IEEE Trans. Automat. Control 40 1889-1904
[6]  
Dai J.G.(1987)The convergence of queueing processes in structurally complex systems with losses to stationary processes Teor. Veroyatnost. i Primenen. 32 577-580
[7]  
Meyn S.P.(1991)On the ergodicity of multichannel not fully accessible communication systems Problems Inform. Transmission 27 94-99
[8]  
Falin G.I.(1996)Stability of multiclass Jackson-type networks Markov Proc. Rel. Fields 2 261-286
[9]  
Foss S.G.(1985)A queueing system with general-use and limited-use servers Oper. Res. 33 168-182
[10]  
Chernova N.I.(1991)Optimality of routing and servicing in dependent parallel processing systems Queueing Systems 9 403-418