We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（...We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.展开更多
The work flow of call center is a typical stochastic service system. This article exploites service rate, which is the most controllable artificial factor of call center, and integrates the abandoning rate of impatien...The work flow of call center is a typical stochastic service system. This article exploites service rate, which is the most controllable artificial factor of call center, and integrates the abandoning rate of impatient customers, models a new-style call center＇s queuing model - the queuing model of M/M/S/K ＋ M based on the impatience and changeable service rate. Then, making use of the traffic forecast result coming from the time series, it models to figure out the numbers of agents per hour, and complete the agents＇ office-hour arrangements in the restriction of some system indexes. Finally, it optimizes the design method by the contrast and analysis of the changeable service rate model and the traditional regular service rate model.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos. 10775104 and 10305009
文摘We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.
文摘The work flow of call center is a typical stochastic service system. This article exploites service rate, which is the most controllable artificial factor of call center, and integrates the abandoning rate of impatient customers, models a new-style call center＇s queuing model - the queuing model of M/M/S/K ＋ M based on the impatience and changeable service rate. Then, making use of the traffic forecast result coming from the time series, it models to figure out the numbers of agents per hour, and complete the agents＇ office-hour arrangements in the restriction of some system indexes. Finally, it optimizes the design method by the contrast and analysis of the changeable service rate model and the traditional regular service rate model.
