On the nonstationary Erlang loss model

Nonstationary loss queueing system (Erlang model) is considered. We study weak ergodicity, bounds on the rate of convergence, approximations, bounds for limit characteristics.

[1]  A I Zeifman On the estimation of probabilities for birth and death process. , 1995, Journal of applied probability.

[2]  Michael Voit,et al.  A note on the rate of convergence to equilibrium for Erlang's model in the subcritical case , 2000, Journal of Applied Probability.

[3]  Александр Израилевич Зейфман,et al.  Оценки и асимптотика скорости сходимости для процессов рождения и гибели@@@Bounds and Asymptotics for the Rate of Convergence of Birth-Death Processes , 2009 .

[4]  Alexander I. Zeifman Some estimates of the rate of convergence for birth and death processes , 1991 .

[5]  T. Ström On Logarithmic Norms , 1975 .

[6]  W. A. Massey,et al.  An Analysis of the Modified Offered-Load Approximation for the Nonstationary Erlang Loss Model , 1994 .

[7]  Boris L. Granovsky,et al.  Nonstationary Queues: Estimation of the Rate of Convergence , 2003, Queueing Syst. Theory Appl..

[8]  Wolfgang Stadje,et al.  Generating function analysis of some joint distributions for Poisson loss systems , 1999, Queueing Syst. Theory Appl..

[9]  Masaaki Kajima On the largest negative eigenvalue of the infinitesimal generator associated with M/M/ n/n queues , 1990 .

[10]  G. Söderlind,et al.  The logarithmic norm. History and modern theory , 2006 .

[11]  B. V. Gnedenko,et al.  Introduction to queueing theory (2nd ed) , 1989 .

[12]  Alexander Zeifman,et al.  On strong ergodicity for nonhomogeneous continuous-time Markov chains , 1994 .

[13]  Alexander I. Zeifman,et al.  On the speed of convergence to stationarity of the Erlang loss system , 2009, Queueing Syst. Theory Appl..

[14]  A. Zeifman Stability of birth-and-death processes , 1998 .

[15]  G. Dahlquist Stability and error bounds in the numerical integration of ordinary differential equations , 1961 .

[16]  Philippe Robert,et al.  On the rates of convergence of Erlang's model , 1999 .

[17]  Alexander I. Zeifman,et al.  Some universal limits for nonhomogeneous birth and death processes , 2006, Queueing Syst. Theory Appl..

[18]  Boris Gnedenko,et al.  Introduction to queueing theory , 1968 .

[19]  Alexander I. Zeifman Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes , 1995 .