Control of Loss Network Systems: Call Admission and Routing Control

In this paper the call admission control (CAC) and routing control (RC) problems for loss network systems are studied as optimal stochastic control (OSC) problems. The socalled pre-state process of the underlying system is a piecewise deterministic Markov process (PDMP) evolving deterministically between (random) event instants at which times the prestate jumps to another value. The random events in the system correspond to the arrival of call requests or the departure of (active) connections. In the principal result the HamiltonJacobi-Bellman (HJB) equations are derived for the underlying stochastic optimal control problems; Unlike the usual single HJB scalar partial difierential equation, we now have a flnite collection of those, inducing coupling within a flnite family of integer indexed value functions. The number of such coupled equations is equal to the number of admissible connection states within the network. Analytical expressions of optimal controls are derived for some simple loss network systems.

[1]  Mark H. Davis.  Markov Models and Optimization , 1995 .

[2]  A. Mullin,et al.  Mathematical Theory of Connecting Networks and Telephone Traffic. , 1966 .

[3]  Peter E. Caines,et al.  Stochastic Hybrid Netcad Systems for Modeling Call Admission and Routing control in Networks , 2006, ADHS.

[4]  John N. Tsitsiklis,et al.  Call admission control and routing in integrated services networks using neuro-dynamic programming , 2000, IEEE Journal on Selected Areas in Communications.

[5]  Peter E. Caines,et al.  On the Viscosity Solutions of Hybrid HJB Equations Arising in Loss Network System Control , 2007 .

[6]  Zhongjing Ma,et al.  Stochastic Control of Network Systems II: NETCAD Optimal Control & the HJB Equation , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[7]  Zbigniew Dziong,et al.  Call admission and routing in multi-service loss networks , 1994, IEEE Trans. Commun..

[8]  Wayne E. Stark,et al.  Stochastic Control of Ad Hoc Communication Networks , 2002 .

[9]  P. Varaiya,et al.  Optimal Control of Jump Processes , 1977 .

[10]  B. Craven.  Control and optimization , 2019, Mathematical Modelling of the Human Cardiovascular System.

[11]  Frank Kelly.  Dynamic Routing in Stochastic Networks , 1995 .

[12]  Peter E. Caines,et al.  On the optimal control of hybrid systems: analysis and zonal algorithms for trajectory and schedule optimization , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[13]  X. Zhou,et al.  Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .

[14]  Zhongjing Ma,et al.  Stochastic Control of Network Systems I: NETCAD State Space Structure & Dynamics , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.