TY - JOUR

T1 - Large Homogeneous communication networks with Markovian access control. I. Equilibria and local stability

AU - Cicero, John

AU - Meerkov, Semyon M.

AU - Schuss, Zeev

N1 - Funding Information:
* Supported by the National Science Foundation under Grant ECS 8 1-16157. + Permanent address: Department of Mathematics, Tel Aviv University, Ramat Aviv, Israel.

PY - 1984/10/30

Y1 - 1984/10/30

N2 - A state space model for a class of Large Homogeneous communication networks with Markovian access control disciplines is considered. It is assumed that each user has a finite or infinite buffer. Asymptotic analysis of the resulting stochastic finite-difference equations reveals the following, previously unknown properties common to all networks in this class: (i) the load line is an algebraic curve of order N, where N is the length of the buffers; (ii) for N = ∞, the average steady state buffer occupancy is yS = y1 (1 - y1) where y1 is the intersection point of the load and transmission lines; an analogous expression is derived also for N < ∞; (iii) the local stability of a steady state is determined by the slopes of the load and transmission lines. Numerical experiments are described to support these findings. The results of this paper give a solution to the problem of dynamic analysis of Large Homogeneous communication networks with Markovian access control disciplines if the steady state is unique. The case of multiple steady states is considered in Part II.

AB - A state space model for a class of Large Homogeneous communication networks with Markovian access control disciplines is considered. It is assumed that each user has a finite or infinite buffer. Asymptotic analysis of the resulting stochastic finite-difference equations reveals the following, previously unknown properties common to all networks in this class: (i) the load line is an algebraic curve of order N, where N is the length of the buffers; (ii) for N = ∞, the average steady state buffer occupancy is yS = y1 (1 - y1) where y1 is the intersection point of the load and transmission lines; an analogous expression is derived also for N < ∞; (iii) the local stability of a steady state is determined by the slopes of the load and transmission lines. Numerical experiments are described to support these findings. The results of this paper give a solution to the problem of dynamic analysis of Large Homogeneous communication networks with Markovian access control disciplines if the steady state is unique. The case of multiple steady states is considered in Part II.

UR - http://www.scopus.com/inward/record.url?scp=0021506766&partnerID=8YFLogxK

U2 - 10.1016/0022-247X(84)90142-2

DO - 10.1016/0022-247X(84)90142-2

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AN - SCOPUS:0021506766

SN - 0022-247X

VL - 103

SP - 481

EP - 496

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -