A two phase batch arrival queueing system with a vacation time under Bernoulli schedule

2004 ◽  
Vol 149 (2) ◽  
pp. 337-349 ◽  
Author(s):  
Gautam Choudhury ◽  
Kailash C. Madan
Keyword(s):  
Queueing System ◽  
Batch Arrival ◽  
Two Phase ◽  
Vacation Time ◽  
Bernoulli Schedule

scholarly journals New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 55 ◽  
Author(s):  
Ilija Tanackov ◽  
Darko Dragić ◽  
Siniša Sremac ◽  
Vuk Bogdanović ◽  
Bojan Matić ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Queueing System ◽  
Analytic Solutions ◽  
Service Discipline ◽  
Second Phase ◽  
Single Server ◽  
Two Phase ◽  
Left Turn ◽  
Unsignalized Intersections ◽  
High Level

Designing the crossroads capacity is a prerequisite for achieving a high level of service with the same sustainability in stochastic traffic flow. Also, modeling of crossroad capacity can influence on balancing (symmetry) of traffic flow. Loss of priority in a left turn and optimal dimensioning of shared-short line is one of the permanent problems at intersections. A shared–short lane for taking a left turn from a priority direction at unsignalized intersections with a homogenous traffic flow and heterogeneous demands is a two-phase queueing system requiring a first in–first out (FIFO) service discipline and single-server service facility. The first phase (short lane) of the system is the queueing system M(pλ)/M(μ)/1/∞, whereas the second phase (shared lane) is a system with a binomial distribution service. In this research, we explicitly derive the probability of the state of a queueing system with a short lane of a finite capacity for taking a left turn and shared lane of infinite capacity. The presented formulas are under the presumption that the system is Markovian, i.e., the vehicle arrivals in both the minor and major streams are distributed according to the Poisson law, and that the service of the vehicles is exponentially distributed. Complex recursive operations in the two-phase queueing system are explained and solved in manuscript.

Two-Phase Queueing System with a Markov Arrival Process and Blocking

2006 ◽  
Vol 132 (5) ◽  
pp. 578-589 ◽  
Author(s):  
P. P. Bocharov ◽  
R. Manzo ◽  
A. V. Pechinkin
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Two Phase ◽  
Markov Arrival ◽  
Markov Arrival Process
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