Sojourn time analysis of a queueing system with two-phase service and server vacations

2007 ◽  
Vol 54 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Tsuyoshi Katayama ◽  
Kaori Kobayashi
Keyword(s):  
Sojourn Time ◽  
Queueing System ◽  
Time Analysis ◽  
Two Phase ◽  
Server Vacations

A two-phase queueing system with server vacations

1994 ◽  
Vol 15 (3) ◽  
pp. 163-168 ◽  
Author(s):  
D. Deivamoney Selvam ◽  
V. Sivasankaran
Keyword(s):  
Queueing System ◽  
Two Phase ◽  
Server Vacations

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

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.

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