TUMOR 发表于 2025-3-21 16:28:36
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Reversible Processes, expected number of the transitions in the reverse order. This is also equivalent to a time-reversibility property that, at any instant, the future of the process is stochastically indistinguishable from viewing the process in reverse time. A remarkable feature of such a process is that its equilibr勉强 发表于 2025-3-22 01:37:44
Miscellaneous Networks,e processes to model networks with multiple types of units, where the routings and services may depend on a customer’s type. This includes Kelly networks with deterministic routes for units, and BCMP networks with Cox and general service times depending on a unit’s type. We also discuss several formOverdose 发表于 2025-3-22 08:24:54
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Little Laws,ttle law. Specifically, a Little law for a service system says that the average sojourn time . of a customer in the system and the average queue length . of the system are related by . = λ., where λ is the average arrival rate of units to the system. This fundamental relation is a . or law of largeMOT 发表于 2025-3-22 15:27:27
Stationary Systems,ulus and Campbell—Mecke formulas for functionals of stationary systems. This material is the foundation for modeling networks and queueing systems with stationary dynamics, and for obtaining Little laws for such systems.含糊 发表于 2025-3-22 19:05:00
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,Space—Time Poisson Models,the collective movement of units or customers in space and time, where the units enter the system according to a Poisson space—time process and then move about independently of each other. Because of these properties, the evolution of the system can be formulated by certain “random transformations”动作谜 发表于 2025-3-23 07:16:26
Spatial Queueing Systems, or a general space. The state of such a system is a point process on a space that evolves over time as a “measure-valued” Markov jump process. Each unit moves in the space according to a Markovian routing mechanism and it receives services at the locations it visits. The service times are exponenti