A single server retrial queue with general retrial times and two-phase service

2009 ◽  
Vol 22 (2) ◽  
pp. 291-302 ◽  
Author(s):  
Jinting Wang ◽  
Jianghua Li
Keyword(s):  
Retrial Queue ◽  
Single Server ◽  
Two Phase

scholarly journals Stochastic Approximations and Monotonicity of a Single Server Feedback Retrial Queue

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Mohamed Boualem ◽  
Natalia Djellab ◽  
Djamil Aïssani
Keyword(s):  
Markov Chains ◽  
Service Time ◽  
Retrial Queue ◽  
Stochastic Ordering ◽  
Stochastic Comparison ◽  
Single Server ◽  
Stochastic Approximations ◽  
Bernoulli Feedback ◽  
Monotonicity Results

This paper focuses on stochastic comparison of the Markov chains to derive some qualitative approximations for anM/G/1retrial queue with a Bernoulli feedback. The main objective is to use stochastic ordering techniques to establish various monotonicity results with respect to arrival rates, service time distributions, and retrial parameters.

Performance Analysis of an M/G/1 Feedback Retrial Queue with Two Types of Service and Bernoulli Vacation

2016 ◽  
pp. 38-54
Author(s):  
Arivudainambi D ◽  
Gowsalya Mahalingam
Keyword(s):  
Retrial Queue ◽  
Single Server ◽  
Supplementary Variable ◽  
Number Of Customers ◽  
Bernoulli Schedule ◽  
Schedule Mechanism ◽  
Fcfs Discipline ◽  
Bernoulli Vacation

This chapter is concerned with the analysis of a single server retrial queue with two types of service, Bernoulli vacation and feedback. The server provides two types of service i.e., type 1 service with probability??1 and type 2 service with probability ??2. We assume that the arriving customer who finds the server busy upon arrival leaves the service area and are queued in the orbit in accordance with an FCFS discipline and repeats its request for service after some random time. After completion of type 1 or type 2 service the unsatisfied customer can feedback and joins the tail of the retrial queue with probability f or else may depart from the system with probability 1–f. Further the server takes vacation under Bernoulli schedule mechanism, i.e., after each service completion the server takes a vacation with probability q or with probability p waits to serve the next customer. For this queueing model, the steady state distributions of the server state and the number of customers in the orbit are obtained using supplementary variable technique. Finally the average number of customers in the system and average number of customers in the orbit are also obtained.

Stability condition for a single-server retrial queue

1993 ◽  
Vol 25 (03) ◽  
pp. 690-701 ◽  
Author(s):  
Huei-Mei Liang ◽  
V. G. Kulkarni
Keyword(s):  
Stability Condition ◽  
Service Time ◽  
Retrial Queue ◽  
Arrival Rate ◽  
Retrial Queues ◽  
Single Server ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Mean ◽  
The Stability

A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system. We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ / μ < 1 is a sufficient stability condition for the M/G /1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

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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