Bin Liu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Bin Liu has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Yiqiang Q. Zhao
School of Mathematics and Statistics, Carleton University, Ottawa, Canada
4 shared publications Yiqiang Q. Zhao
School of Mathematics and Statistics Carleton University K1S 5B6 Ottawa ON CANADA
2 shared publicationsJie Min
School of Mathematics & Physics Anhui Jianzhu University 230601 Hefei P.R.China
1 shared publication- Jie Min
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
1 shared publication
Latest Publications
- 28 March 2023
- Published by Springer Nature in Queueing Systems
- Vol. 104 (1-2) , 65-105
Refined tail asymptotic properties for the $M^X/G/1$ retrial queue- 28 March 2023
- Published by Springer Nature in Queueing Systems
- Vol. 104 (1-2) , 65-105
Refined tail asymptotic properties for the $M^X/G/1$ retrial queue- Open Access
- 7 August 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (15) , 2799
Tail Asymptotics for a Retrial Queue with Bernoulli Schedule
In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the conditional probability of the number of customers in the (priority) queue and orbit, respectively, in terms of the recently proposed exhaustive stochastic decomposition approach. Numerical examples are presented to show the impacts of system parameters on the tail asymptotic probabilities.- 7 August 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (15) , 2799
Open AccessTail Asymptotics for a Retrial Queue with Bernoulli Schedule
In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the conditional probability of the number of customers in the (priority) queue and orbit, respectively, in terms of the recently proposed exhaustive stochastic decomposition approach. Numerical examples are presented to show the impacts of system parameters on the tail asymptotic probabilities. - 29 September 2020
- Published by Springer Nature in Queueing Systems
- Vol. 96 (1-2) , 169-199
Tail asymptotics for the $M_1,M_2/G_1,G_2/1$ retrial queue with non-preemptive priority- 29 September 2020
- Published by Springer Nature in Queueing Systems
- Vol. 96 (1-2) , 169-199
Tail asymptotics for the $M_1,M_2/G_1,G_2/1$ retrial queue with non-preemptive priority- Open AccessRefined Tail Asymptotic Properties for the $M^X/G/1$ Retrial QueueIn the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The equivalence theorem provides the distribution (or tail) equivalence between the total number of customers in the system for the retrial queue and the total number of customers in the corresponding standard (non-retrial) queue. In this paper, under the assumption of regularly varying tails, we eliminate this condition by allowing that the service time can be either heavier or lighter than the batch size. The main contribution made in this paper is an asymptotic characterization of the difference between two tail probabilities: the probability of the total number of customers in the system for the $M^X/G/1$ retrial queue and the probability of the total number of customers in the corresponding standard (non-retrial) queue. The equivalence theorem by allowing a heavier batch size is another contribution in this paper.Open AccessRefined Tail Asymptotic Properties for the $M^X/G/1$ Retrial QueueIn the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The equivalence theorem provides the distribution (or tail) equivalence between the total number of customers in the system for the retrial queue and the total number of customers in the corresponding standard (non-retrial) queue. In this paper, under the assumption of regularly varying tails, we eliminate this condition by allowing that the service time can be either heavier or lighter than the batch size. The main contribution made in this paper is an asymptotic characterization of the difference between two tail probabilities: the probability of the total number of customers in the system for the $M^X/G/1$ retrial queue and the probability of the total number of customers in the corresponding standard (non-retrial) queue. The equivalence theorem by allowing a heavier batch size is another contribution in this paper.
- 16 October 2019
- Published by Springer Nature
- p. 361-373
Tail Asymptotics for the Waiting Time in an M/G/1/ROS Vacation Queue with Regularly-Varying Service
- 16 October 2019
- Published by Springer Nature
- p. 361-373
Tail Asymptotics for the Waiting Time in an M/G/1/ROS Vacation Queue with Regularly-Varying Service
- Open Access
Tail Asymptotics for a Retrial Queue with Bernoulli Schedule
In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state $M/G/1$ retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the (conditional and unconditional) probability of the number of customers in the (priority) queue, orbit and system, respectively.Open AccessTail Asymptotics for a Retrial Queue with Bernoulli Schedule
In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state $M/G/1$ retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the (conditional and unconditional) probability of the number of customers in the (priority) queue, orbit and system, respectively. - Open AccessTail Asymptotics for the $M_1,M_2/G_1,G_2/1$ Retrial Queue with Priority
Stochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: the retrial queueing systems with priority. This type of queueing system is important in various applications, including telecommunication and computer management networks with big data. For this type of system, we propose a detailed stochastic decomposition approach to study its asymptotic behaviour of the tail probability of the number of customers in the steady-state for retrial queues with two types (Type-1 and Type-2) of customers, in which Type-1 customers (in a queue) have non-preemptive priority to receive service over Type-2 customers (in an orbit). Under the assumption that the service times of Type-1 customers have a regularly varying tail and the service times of Type-2 customers have a tail lighter than Type-1 customers, we obtain tail asymptotic properties for the number of customers in the queue and in the orbit, respectively, conditional on the server's status, in terms of a detailed stochastic decomposition approach. Tail asymptotic properties are often used as key tools for approximating various performance metrics and constructing numerical algorithms for computations.
Open AccessTail Asymptotics for the $M_1,M_2/G_1,G_2/1$ Retrial Queue with PriorityStochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: the retrial queueing systems with priority. This type of queueing system is important in various applications, including telecommunication and computer management networks with big data. For this type of system, we propose a detailed stochastic decomposition approach to study its asymptotic behaviour of the tail probability of the number of customers in the steady-state for retrial queues with two types (Type-1 and Type-2) of customers, in which Type-1 customers (in a queue) have non-preemptive priority to receive service over Type-2 customers (in an orbit). Under the assumption that the service times of Type-1 customers have a regularly varying tail and the service times of Type-2 customers have a tail lighter than Type-1 customers, we obtain tail asymptotic properties for the number of customers in the queue and in the orbit, respectively, conditional on the server's status, in terms of a detailed stochastic decomposition approach. Tail asymptotic properties are often used as key tools for approximating various performance metrics and constructing numerical algorithms for computations.