“…These cooperations could be just between neighbours or amongst all the customers awaiting service. Zero-automatic queues [7], for example, allow neighbouring customers of a shared group of classes to interact and coalesce into a single customer.…”
Queueing network formalisms are very good at describing the spatial movement of customers, but typically poor at describing how customers change as they move through the network. We present the PEPA Queues formalism, which uses the popular stochastic process algebra PEPA to represent the individual state and behaviour of customers and servers. We offer a formal semantics for PEPA Queues, plus a direct translation to PEPA, allowing access to the existing tools for analysing PEPA models. Finally, we use the ipc/DNAmaca tool-chain to provide passage-time analysis of a dual Web server example.
“…These cooperations could be just between neighbours or amongst all the customers awaiting service. Zero-automatic queues [7], for example, allow neighbouring customers of a shared group of classes to interact and coalesce into a single customer.…”
Queueing network formalisms are very good at describing the spatial movement of customers, but typically poor at describing how customers change as they move through the network. We present the PEPA Queues formalism, which uses the popular stochastic process algebra PEPA to represent the individual state and behaviour of customers and servers. We offer a formal semantics for PEPA Queues, plus a direct translation to PEPA, allowing access to the existing tools for analysing PEPA models. Finally, we use the ipc/DNAmaca tool-chain to provide passage-time analysis of a dual Web server example.
We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable 0-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of 0-automatic queues, we recover the simple M/M/1 queue, and Gelenbe's G-queue with positive and negative customers.
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