Analysis of an N-policy MX/M/1 Two-phase Queueing System with State-dependent Arrival Rates and Unreliable Server

This work considers a queueing system with N-policy and unreliable server, where potential customers arrive at the system according to Poisson process. If there is no customer waiting in the system, instead of shutting down, the server turns into dormant state and does not afford service until the number of customers is accumulated to a certain threshold. And in the working state, the server is apt to breakdown and affords service again only after it is repaired. According to whether the server state is observable or not, the numerical optimal arrival rates are computed to maximize the social welfare and throughput of the system. The results illustrate their tendency in two cases so that the manager has a strong ability to decide which is more crucial in making management decision.

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Optimal design for a retrial queueing system with state-dependent service rate

Journal of Systems Science and Complexity ◽

10.1007/s11424-017-5097-9 ◽

2017 ◽

Vol 30 (4) ◽

pp. 883-900 ◽

Cited By ~ 4

Author(s):

Xuelu Zhang ◽

Jinting Wang ◽

Qing Ma

Keyword(s):

Optimal Design ◽

Queueing System ◽

Service Rate ◽

Retrial Queueing System ◽

State Dependent ◽

Retrial Queueing

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

Symmetry ◽

10.3390/sym11010055 ◽

2019 ◽

Vol 11 (1) ◽

pp. 55 ◽

Cited By ~ 1

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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