In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time an...In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time and the vacation time follow exponential distributions.The authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the system.Then,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is obtained.Furthermore,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are derived.Using the stationary distribution,the authors obtain some performance measures of the system.The authors investigate analytically the effect of the server’s vacation on the performance measures.Finally,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.展开更多
The analysis and evaluation of an actual port system containing R differentship’s kinds and N subsystems each of which consists of M.(i=1, 2,…, N) ports arederived. The external arrivals of ships to the system come ...The analysis and evaluation of an actual port system containing R differentship’s kinds and N subsystems each of which consists of M.(i=1, 2,…, N) ports arederived. The external arrivals of ships to the system come from R different Poisson sourcesand the interarrivals to the queue of each port of a subsystem are determined according tocondition probabilities. Each port has multiple berths whose service times are distributedaccording to Erlang probability distribution functions. Each port of a subsystem has Rinfinite capacity buffers for storing ships interarrived. This method provides a good approximation procedure for obtaining system perfor-mance measures such as waiting times of ships, average queue lengths, etc. Optimum portcapacity can thus be evaluated by using this analysis. A simulation is also presented totest this approximate analysis, and a good agreement is observed. This model shall be usedin the planning of several actual port systems. Through the application of this model, itis possible to analyze and evaluate performances of the systems.展开更多
基金supported in part by the Natural Science Foundation of China under Grant No.71971189the Natural Science Foundation of Hebei Province under Grant No.A2019203313+1 种基金the Key Project of Scientific Research in Higher Education of Hebei Province of China under Grant No.ZD2018042in part by MEXT,Japan。
文摘In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time and the vacation time follow exponential distributions.The authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the system.Then,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is obtained.Furthermore,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are derived.Using the stationary distribution,the authors obtain some performance measures of the system.The authors investigate analytically the effect of the server’s vacation on the performance measures.Finally,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.
文摘The analysis and evaluation of an actual port system containing R differentship’s kinds and N subsystems each of which consists of M.(i=1, 2,…, N) ports arederived. The external arrivals of ships to the system come from R different Poisson sourcesand the interarrivals to the queue of each port of a subsystem are determined according tocondition probabilities. Each port has multiple berths whose service times are distributedaccording to Erlang probability distribution functions. Each port of a subsystem has Rinfinite capacity buffers for storing ships interarrived. This method provides a good approximation procedure for obtaining system perfor-mance measures such as waiting times of ships, average queue lengths, etc. Optimum portcapacity can thus be evaluated by using this analysis. A simulation is also presented totest this approximate analysis, and a good agreement is observed. This model shall be usedin the planning of several actual port systems. Through the application of this model, itis possible to analyze and evaluate performances of the systems.
