We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λz, i...We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λz, is firstly revealed. A criterion regarding ）λz-recurrence and λz-positive is obtained. The corresponding λz-subinvariant/invariant measures and λz-subinvariant/invariant vectors are then presented.展开更多
A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers dem...A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first ＂essential＂ service, whereas only some of them demand the second ＂multi-optional＂ service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a servicephase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.展开更多
We consider a multiclass service system with refusal and bulk-arrival. The properties regarding recurrence, ergodicity, and decay properties of such model are discussed. The explicit criteria regarding recurrence and ...We consider a multiclass service system with refusal and bulk-arrival. The properties regarding recurrence, ergodicity, and decay properties of such model are discussed. The explicit criteria regarding recurrence and ergodicity are obtained. The stationary distribution is given in the ergodic case. Then, the exact value of the decay parameter, denoted by λE, is obtained in the transient case. The criteria for the λE-recurrence are also obtained. Finally, the corresponding λE-invariant vector/measure is considered.展开更多
We consider an MX/M/c queue with catastrophes and state- dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, a...We consider an MX/M/c queue with catastrophes and state- dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing MX/M/c queue.展开更多
文摘We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λz, is firstly revealed. A criterion regarding ）λz-recurrence and λz-positive is obtained. The corresponding λz-subinvariant/invariant measures and λz-subinvariant/invariant vectors are then presented.
基金Supported by the National Natural Science Foundation of China (No. 10871020)
文摘A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first ＂essential＂ service, whereas only some of them demand the second ＂multi-optional＂ service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a servicephase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.
文摘We consider a multiclass service system with refusal and bulk-arrival. The properties regarding recurrence, ergodicity, and decay properties of such model are discussed. The explicit criteria regarding recurrence and ergodicity are obtained. The stationary distribution is given in the ergodic case. Then, the exact value of the decay parameter, denoted by λE, is obtained in the transient case. The criteria for the λE-recurrence are also obtained. Finally, the corresponding λE-invariant vector/measure is considered.
基金This work was substantially supported by the National Natural Sciences Foundations of China （Grant Nos. 11371374, 11771452, 11701489, 11571372）, the National Natural Science Foundation of China-Tian Yuan （Grant No. 11626203）, and the Natural Sciences Foundations of Hunan Province （No. 2017JJ2328）.
文摘We consider an MX/M/c queue with catastrophes and state- dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing MX/M/c queue.
