Stability of the free equilibrium state of a nonlinear age structured model for a two-sex population

2025-12-04T09:40:13+00:00

This paper focuses on the study of the stability of the free equilibrium state of a nonlinear
age structured model. The spectral properties of semigroup, the Riesz-Fréchet-Kolmogorov
(RFK) criterion in L² combined to the Calkin algebra theory are used to obtain the stability result
of the free equilibrium state.

Modeling of Telecommunication Networks by M/M/K (K > 2) Queueing Systems with Impatient Customers

2025-12-03T21:39:42+00:00

The objective of this work is to apply the M/M/K (K > 2) queueing network model to better understand the problem of saturation and disruption in telecommunication networks. Assuming that the system has reached an equilibrium between arrivals and departures, we derive the system of equations associated with the model. By using the probability generating function method, we obtain the network availability probability as well as key performance metrics such as the average number of calls waiting for connection and the average call duration before connection (using Little’s formula). Through numerical illustrations, we show, on the one hand, the influence of the parameters α (arrival rate), μ (service rate), and ε (impatience threshold) on the network availability probability P0;0, and on the other hand, the impact of P0;0 on the average call duration before connection.

Journal de Mathématiques Pures et Appliquées de Ouagadougou (JMPAO)

Stability of the free equilibrium state of a nonlinear age structured model for a two-sex population

Modeling of Telecommunication Networks by M/M/K (K > 2) Queueing Systems with Impatient Customers