Inference for cluster point processes with over- or under-dispersed cluster sizes

A road traffic model with restricted passing, formulated by Newell (1966), is described by conditional cluster point processes and analytically handled by generating functionals of point processes.The traffic distributions in either space or time are in equilibrium, if the fast cars form a Poisson process with constant intensity combined with Poisson-distributed queues behind the slow cars (Brill (1971)). It is shown that this state of equilibrium is stable, which means that this state will be reached asymptotically for general initial traffic distributions. Furthermore the queues behind the slow cars dissolve asymptotically like independent Poisson processes with diminishing rate, also independent of the process of non-queuing cars. To get these results limit theorems for conditional cluster point processes are formulated.

Download Full-text

Optimal stopping and cluster point processes

Statistics & Decisions ◽

10.1524/stnd.21.3.261.23431 ◽

2003 ◽

Vol 21 (3-2003) ◽

pp. 261-282 ◽

Cited By ~ 3

Author(s):

Robert Kühne ◽

Ludger Rüschendorf

Keyword(s):

Optimal Stopping ◽

Point Processes ◽

Cluster Point

Download Full-text

Central Limit Theorems for Cluster Point Processes

Advances in the Statistical Sciences: Applied Probability, Stochastic Processes, and Sampling Theory ◽

10.1007/978-94-009-4786-3_10 ◽

1987 ◽

pp. 131-139

Author(s):

R. J. Kulperger

Keyword(s):

Central Limit ◽

Limit Theorems ◽

Point Processes ◽

Central Limit Theorems ◽

Cluster Point

Download Full-text

Software reliability growth models based on cluster point processes

International Journal of Systems Science ◽

10.1080/00207729408928992 ◽

1994 ◽

Vol 25 (4) ◽

pp. 737-751 ◽

Cited By ~ 9

Author(s):

PANLOP ZEEPHONGSEKUL ◽

GUOLIN XIA ◽

SANTOSH KUMAR

Keyword(s):

Software Reliability ◽

Point Processes ◽

Growth Models ◽

Cluster Point ◽

Reliability Growth ◽

Software Reliability Growth Models ◽

Software Reliability Growth

Download Full-text

Convergence to equilibrium in a traffic model with restricted passing

Journal of Applied Probability ◽

10.1017/s0021900200033568 ◽

1979 ◽

Vol 16 (04) ◽

pp. 881-889 ◽

Cited By ~ 1

Author(s):

Hans Dieter Unkelbach

Keyword(s):

Poisson Process ◽

Limit Theorems ◽

Point Processes ◽

Road Traffic ◽

Poisson Processes ◽

Traffic Model ◽

Cluster Point ◽

Convergence To Equilibrium ◽

Constant Intensity

A road traffic model with restricted passing, formulated by Newell (1966), is described by conditional cluster point processes and analytically handled by generating functionals of point processes. The traffic distributions in either space or time are in equilibrium, if the fast cars form a Poisson process with constant intensity combined with Poisson-distributed queues behind the slow cars (Brill (1971)). It is shown that this state of equilibrium is stable, which means that this state will be reached asymptotically for general initial traffic distributions. Furthermore the queues behind the slow cars dissolve asymptotically like independent Poisson processes with diminishing rate, also independent of the process of non-queuing cars. To get these results limit theorems for conditional cluster point processes are formulated.

Download Full-text