The discussion moves from the Poisson process, which is pure birth process to birth and death processes, which model basic queuing systems. The method of stages is introduced as a way to generalize the service time distribution from the exponential to an arbitrary distribution. The technique is ...
Here we will focus on a specific subset of Markov Chains, the so-called birth–death processes, which well match with the memoryless property of the Poisson process and of the negative exponential distribution. The general model described in this chapter will be re-used in the remainder of ...
1) birth-death process 生灭过程 1. Firstly,the system state probability is estimated by Markov birth-death process,and then the request loss probability in stable system states is estimated by queuing theory,lastly, combining both of them,therefore the expression for the user perceived ...
Instead, start from first principles. (1) You have a birth-death process. (2) Draw the transition diagram. (3) Write down in detail, one-by-one, the steady-state equations. (4) Solve the equations [NOT difficul!].FAQ: Birth Death Model: M/M/C Queueing System ...
A birth and death process related to the Rogers-Ramanujan continued fraction. J. Math. Anal. Appl., 224:297-315, 1998.P. R. Parthasarathy,,R. B. Lenin,,W. Schoutens,W. Van Assche.A birth and death process related to the Rogers-Ramanujan continued fraction. Journal of Mathematical ...
Birth–death processesQueuing theoryIntegrals of Markov processesIn this paper a regenerative argument is used to derive an expression for the expectation of the integral under the stochastic path of a birth–death Markov process up to extinction time as well as for the expected time to extinction...
QUEUING theoryMANAGEMENT scienceSTOCHASTIC processesMARKOV processesMATHEMATICAL analysisWe consider a class of birth and death processes with finally constant birth and death intensities and obtain the exact formula for spectral gap of the process in some situations. Moreover, we study spectral gap ...
4) birth-death process 生灭过程 1. Firstly,the system state probability is estimated by Markovbirth-death process,and then the request loss probability in stable system states is estimated by queuing theory,lastly, combining both of them,therefore the expression for the user perceived availability ...
1) Markov birth-death process Markov生灭过程 1. By analyzing the pollution origination and propagation in peer-to-peer(P2P)network,a pollution propagation model is established based on the Markov birth-death process. 分析P2P网络文件污染的产生和传播机制,建立基于Markov生灭过程的污染传播模型,推导出...