Uniform Estimation of the Convergence Rate in a Renewal Theorem for the Case of Discrete Time

1978 ◽  
Vol 22 (2) ◽  
pp. 390-394 ◽  
Author(s):  
V. V. Kalashnikov
Keyword(s):  
Convergence Rate ◽  
Discrete Time ◽  
Renewal Theorem

The stationary tail asymptotics in the GI/G/1-type queue with countably many background states

2004 ◽  
Vol 36 (4) ◽  
pp. 1231-1251 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Yiqiang Q. Zhao
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Priority Queue ◽  
Decay Rates ◽  
Single Server ◽  
Renewal Theorem ◽  
Tail Probabilities ◽  
Markov Renewal Equation ◽  
Geometric Decay ◽  
Background State

We consider the asymptotic behaviour of the stationary tail probabilities in the discrete-time GI/G/1-type queue with countable background state space. These probabilities are presented in matrix form with respect to the background state space, and shown to be the solution of a Markov renewal equation. Using this fact, we consider their decay rates. Applying the Markov renewal theorem, it is shown that certain reasonable conditions lead to the geometric decay of the tail probabilities as the level goes to infinity. We exemplify this result using a discrete-time priority queue with a single server and two types of customer.

The stationary tail asymptotics in the GI/G/1-type queue with countably many background states

2004 ◽  
Vol 36 (04) ◽  
pp. 1231-1251 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Yiqiang Q. Zhao
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Priority Queue ◽  
Decay Rates ◽  
Single Server ◽  
Renewal Theorem ◽  
Tail Probabilities ◽  
Markov Renewal Equation ◽  
Geometric Decay ◽  
Background State

We consider the asymptotic behaviour of the stationary tail probabilities in the discrete-time GI/G/1-type queue with countable background state space. These probabilities are presented in matrix form with respect to the background state space, and shown to be the solution of a Markov renewal equation. Using this fact, we consider their decay rates. Applying the Markov renewal theorem, it is shown that certain reasonable conditions lead to the geometric decay of the tail probabilities as the level goes to infinity. We exemplify this result using a discrete-time priority queue with a single server and two types of customer.

scholarly journals Consensus of Discrete Time Second-Order Multiagent Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhu
Keyword(s):  
Time Delay ◽  
Convergence Rate ◽  
Theoretical Result ◽  
Multiagent Systems ◽  
Discrete Time ◽  
Second Order ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The consensus problem for discrete time second-order multiagent systems with time delay is studied. Some effective methods are presented to deal with consensus problems in discrete time multiagent systems. A necessary and sufficient condition is established to ensure consensus. The convergence rate for reaching consensus is also estimated. It is shown that arbitrary bounded time delay can safely be tolerated. An example is presented to illustrate the theoretical result.

scholarly journals Estimates of the convergence rate in the limit theorems on transition phenomena for branching random processes

2021 ◽  
pp. 15-28
Author(s):  
Ш.Ю. Жураев ◽  
А.Ф. Алиев
Keyword(s):  
Convergence Rate ◽  
Discrete Time ◽  
Limit Theorems ◽  
Random Processes ◽  
Initial Moment ◽  
Conditional Distributions ◽  
Number Of Particles

В данной работе рассматриваются ветвящиеся случайные процессы с дискретным временем в двух предположениях: в начальный момент времени имеется одна частица или в начальный момент времени существует большое число частиц. В переходных явлениях для таких ветвящихся случайных процессов получены оценки скорости сходимости условных законов распределений к предельному распределению. We consider branching random processes with discrete time in two assumptions: at the initial moment of time there is one particle and there are large number of particles. In transition phenomena for such branching random processes, estimates of the convergence rate of conditional distributions are obtained.

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