We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponen...We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.展开更多
In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a...In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.展开更多
We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson stream...We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.展开更多
In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the...In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the six models analysed, the Laplace-Stieltjes transform of the virtual waiting time Wk(t) at time t of class k is derived by the method of collective marks. A sufficient condition for , where U has the standard normal distribution, is also given.展开更多
This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving pr...This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving process with different rates. The channel holding times of the two types of calls follow different phase-type distributions. Firstly, the joint distribution of two queue lengths is derived, and then the dropping and blocking probabilities, the mean queue length and the mean waiting time from the joint distribution are gotten. Finally, numerical examples show the impact of different call arrival rates on the performance measures.展开更多
In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodol...In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodology for applying these theorems for the benefit of service systems. The limit theorems studied here are dominant in the literature. Our contribution is primarily on the analysis leading to the application of these theorems in various problem situations for better operations. Relevant Examples are included to aid the application of the results studied in this work.展开更多
This paper presents mathematical models and optimal algorithms of two FIFO-queues control in single-level memory. These models are designed as two-dimensional random walks on the integer lattice in a rectangular area ...This paper presents mathematical models and optimal algorithms of two FIFO-queues control in single-level memory. These models are designed as two-dimensional random walks on the integer lattice in a rectangular area for consecutive implementation and a triangle area for linked list implementation.展开更多
In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to st...In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11971486)。
文摘We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.
基金Supported by the National Natural Science Foundation of China(11571372,11771452)the Innovation Program of Central South University(10900-50601010)
文摘In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.
文摘We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.
文摘In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the six models analysed, the Laplace-Stieltjes transform of the virtual waiting time Wk(t) at time t of class k is derived by the method of collective marks. A sufficient condition for , where U has the standard normal distribution, is also given.
基金supported by the Postgraduate Innovation Project of Jiangsu University (CX10B 003X)
文摘This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving process with different rates. The channel holding times of the two types of calls follow different phase-type distributions. Firstly, the joint distribution of two queue lengths is derived, and then the dropping and blocking probabilities, the mean queue length and the mean waiting time from the joint distribution are gotten. Finally, numerical examples show the impact of different call arrival rates on the performance measures.
文摘In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodology for applying these theorems for the benefit of service systems. The limit theorems studied here are dominant in the literature. Our contribution is primarily on the analysis leading to the application of these theorems in various problem situations for better operations. Relevant Examples are included to aid the application of the results studied in this work.
文摘This paper presents mathematical models and optimal algorithms of two FIFO-queues control in single-level memory. These models are designed as two-dimensional random walks on the integer lattice in a rectangular area for consecutive implementation and a triangle area for linked list implementation.
文摘In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.
