Control of Admission and Routing in Loss Networks: Hybrid Dynamic Programming Equations
Call admission and routing control decisions in stochastic loss (circuit-switched) networks with semi Markovian, multi-class, call arrival and general connection time processes are formulated as optimal stochastic control problems. The resulting so-called Hybrid Dynamic Programming equation systems...
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| Veröffentlicht in: | IEEE transactions on automatic control 2010-02, Vol.55 (2), p.350-366 |
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| container_title | IEEE transactions on automatic control |
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| creator | Zhongjing Ma Caines, P.E. Malhame, R.P. |
| description | Call admission and routing control decisions in stochastic loss (circuit-switched) networks with semi Markovian, multi-class, call arrival and general connection time processes are formulated as optimal stochastic control problems. The resulting so-called Hybrid Dynamic Programming equation systems take the form of vectors of partial differential equations with each component associated to a distinct distribution of routed calls over the network (i.e. distinct occupation states). This framework reduces to that of a Markov Decision Process when the traffic is Poisson and the associated computational limitations are approximately those of linear programs. Examples are provided of (i) network state space constructions and controlled state transition processes, (ii) a new closed form solution for a simple network, and (iii) the analysis and illustrative numerical results for a three link network. |
| doi_str_mv | 10.1109/TAC.2009.2034934 |
| format | Article |
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The resulting so-called Hybrid Dynamic Programming equation systems take the form of vectors of partial differential equations with each component associated to a distinct distribution of routed calls over the network (i.e. distinct occupation states). This framework reduces to that of a Markov Decision Process when the traffic is Poisson and the associated computational limitations are approximately those of linear programs. Examples are provided of (i) network state space constructions and controlled state transition processes, (ii) a new closed form solution for a simple network, and (iii) the analysis and illustrative numerical results for a three link network.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2009.2034934</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Call admission and routing control ; Circuits ; Communication system traffic control ; Computer networks ; Computer science; control theory; systems ; Computer systems and distributed systems. User interface ; Control theory. 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The resulting so-called Hybrid Dynamic Programming equation systems take the form of vectors of partial differential equations with each component associated to a distinct distribution of routed calls over the network (i.e. distinct occupation states). This framework reduces to that of a Markov Decision Process when the traffic is Poisson and the associated computational limitations are approximately those of linear programs. Examples are provided of (i) network state space constructions and controlled state transition processes, (ii) a new closed form solution for a simple network, and (iii) the analysis and illustrative numerical results for a three link network.</description><subject>Applied sciences</subject><subject>Call admission and routing control</subject><subject>Circuits</subject><subject>Communication system traffic control</subject><subject>Computer networks</subject><subject>Computer science; control theory; systems</subject><subject>Computer systems and distributed systems. User interface</subject><subject>Control theory. Systems</subject><subject>Decisions</subject><subject>Differential equations</subject><subject>Dynamic programming</subject><subject>Exact sciences and technology</subject><subject>Exact solutions</subject><subject>Game theory</subject><subject>hybrid dynamic programming (HDP) equations</subject><subject>loss networks</subject><subject>Mathematical analysis</subject><subject>Networks</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Optimal control</subject><subject>Partial differential equations</subject><subject>Poisson equations</subject><subject>Routing</subject><subject>Routing (telecommunications)</subject><subject>Software</subject><subject>Stochastic processes</subject><subject>Stochasticity</subject><subject>Vectors</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkUtLAzEUhYMoWB97wU0QxNVo3pO4K7U-oKhIwWVIp4lEZxJNZpD-e1NaXLiRwA2X-90D9xwATjC6xBipq_l4ckkQUqVQpijbASPMuawIJ3QXjBDCslJEin1wkPN7aQVjeAReJzH0KbYwOjhedj5nHwM0YQlf4tD78AZ9gLOYM3y0_XdMH_ka3q8WyS_hzSqYzjfwOcW3ZLpuDU-_BtMXhXwE9pxpsz3e_odgfjudT-6r2dPdw2Q8qxoqWV8JbCmmBLOFK2-JLBVIsVpQYpxruHBEOWUEptwQJRlHktmmtgQxVxNn6CG42Mh-pvg12NzrckJj29YEG4esZc0RIRyrf8maUcExRWvy7A_5HocUyhVaciEQLTYXCG2gJhVzknX6M_nOpJXGSK8D0SUQvQ5EbwMpK-dbXZMb07pkQuPz7x4hjGCCZOFON5y31v6OOS0uFGN-AMepkhA</recordid><startdate>20100201</startdate><enddate>20100201</enddate><creator>Zhongjing Ma</creator><creator>Caines, P.E.</creator><creator>Malhame, R.P.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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User interface</topic><topic>Control theory. Systems</topic><topic>Decisions</topic><topic>Differential equations</topic><topic>Dynamic programming</topic><topic>Exact sciences and technology</topic><topic>Exact solutions</topic><topic>Game theory</topic><topic>hybrid dynamic programming (HDP) equations</topic><topic>loss networks</topic><topic>Mathematical analysis</topic><topic>Networks</topic><topic>Operational research and scientific management</topic><topic>Operational research. 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| subjects | Applied sciences Call admission and routing control Circuits Communication system traffic control Computer networks Computer science control theory systems Computer systems and distributed systems. User interface Control theory. Systems Decisions Differential equations Dynamic programming Exact sciences and technology Exact solutions Game theory hybrid dynamic programming (HDP) equations loss networks Mathematical analysis Networks Operational research and scientific management Operational research. Management science Optimal control Partial differential equations Poisson equations Routing Routing (telecommunications) Software Stochastic processes Stochasticity Vectors |
| title | Control of Admission and Routing in Loss Networks: Hybrid Dynamic Programming Equations |
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