Copula Analysis of Temporal Dependence Structure in Markov Modulated Poisson Process and Its Applications

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

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Markov modulated Poisson process model for hand-off calls in cellular systems

2000 IEEE Wireless Communications and Networking Conference. Conference Record (Cat. No.00TH8540) ◽

10.1109/wcnc.2000.904784 ◽

2002 ◽

Cited By ~ 10

Author(s):

M.A. Farahani ◽

M. Guizani

Keyword(s):

Poisson Process ◽

Process Model ◽

Cellular Systems ◽

Markov Modulated Poisson Process ◽

Hand Off ◽

Markov Modulated

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A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

Journal of Applied Probability ◽

10.1017/s0021900200103572 ◽

1995 ◽

Vol 32 (04) ◽

pp. 1103-1111 ◽

Cited By ~ 1

Author(s):

Qing Du

Keyword(s):

Poisson Process ◽

Arrival Rate ◽

Loss Probability ◽

Arrival Process ◽

Single Server ◽

Single Server Queue ◽

Markov Modulated Poisson Process ◽

Server Queue ◽

Monotonicity Result ◽

Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i . The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i . In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

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Renewal characterization of Markov modulated Poisson processes

Journal of Applied Mathematics and Simulation ◽

10.1155/s1048953389000043 ◽

1989 ◽

Vol 2 (1) ◽

pp. 53-70 ◽

Cited By ~ 3

Author(s):

Marcel F. Neuts ◽

Ushio Sumita ◽

Yoshitaka Takahashi

Keyword(s):

Markov Chain ◽

Poisson Process ◽

Renewal Process ◽

Jump Process ◽

Probability Vector ◽

Markov Modulated Poisson Process ◽

Markov Modulated ◽

Bivariate Markov Chain ◽

Characterization Theorems

A Markov Modulated Poisson Process (MMPP) M(t) defined on a Markov chain J(t) is a pure jump process where jumps of M(t) occur according to a Poisson process with intensity λi whenever the Markov chain J(t) is in state i. M(t) is called strongly renewal (SR) if M(t) is a renewal process for an arbitrary initial probability vector of J(t) with full support on P={i:λi>0}. M(t) is called weakly renewal (WR) if there exists an initial probability vector of J(t) such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class SR and some sufficiency theorems for the class WR in terms of the first passage times of the bivariate Markov chain [J(t),M(t)]. Relevance to the lumpability of J(t) is also studied.

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