A unified approach to computation of integrable structures

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based approach and aim to provide a tutorial to the computations.Comment: 19 pages, based on a talk on the SPT 2011 conference, http://www.sptspt.it/spt2011/ ; v2, v3: minor correction

A single-server finite-capacity queueing system with Markov flow and discrete-time service

Concepts of a discrete Markov flow and discrete-time Markov service are defined. A single-server finite-capacity queueing system with Markov flow and discrete-time service is studied. An algorithm for computing the stationary state probability distribution of the system is designed. The main performance characteristics, such as the stationary loss probability and mean waiting time for service, are determined. © 2005 Pleiades Publishing, Inc

A single-server finite-capacity queueing system with Markov flow and discrete-time service

Concepts of a discrete Markov flow and discrete-time Markov service are defined. A single-server finite-capacity queueing system with Markov flow and discrete-time service is studied. An algorithm for computing the stationary state probability distribution of the system is designed. The main performance characteristics, such as the stationary loss probability and mean waiting time for service, are determined. © 2005 Pleiades Publishing, Inc

Exponential queuing network with dependent servicing, negative customers, and modification of the customer type

The open exponential queuing network with negative customers (G-network) was considered. For each arriving customer, given was a set of its random parameters such as the route defining the sequence of network nodes passed by the customer, route length, size, and servicing duration at each stage of the route. It was assumed that the negative customer arriving to the sth node with the probabilities ωs and ωs + either kills the positive customer in a randomly chosen server or does not affect it at all and with the probability ωs - = 1 - ωs - ωs + transforms it into a negative customer which after an exponentially distributed time arrives to the s′th node with the given probability. The multidimensional stationary probability distribution of the network states was proved to be representable in the multiplicative form

Exponential queueing network with dependent discipline, negative requests, and variable request types

An open exponential queueing network with negative requests (G-network) is considered. A set of random parameters is given for each request entering the network: its route along the network, governing the units sequence passed by the request, the route length, request body and its servicing duration of every route stage. The multidimensional stationary distribution of state probabilities of the considered network is represented in the multiplicative form

Exponential queuing network with dependent servicing, negative customers, and modification of the customer type

The open exponential queuing network with negative customers (G-network) was considered. For each arriving customer, given was a set of its random parameters such as the route defining the sequence of network nodes passed by the customer, route length, size, and servicing duration at each stage of the route. It was assumed that the negative customer arriving to the sth node with the probabilities ωs and ωs + either kills the positive customer in a randomly chosen server or does not affect it at all and with the probability ωs - = 1 - ωs - ωs + transforms it into a negative customer which after an exponentially distributed time arrives to the s′th node with the given probability. The multidimensional stationary probability distribution of the network states was proved to be representable in the multiplicative form

Exponential queueing network with dependent discipline, negative requests, and variable request types

An open exponential queueing network with negative requests (G-network) is considered. A set of random parameters is given for each request entering the network: its route along the network, governing the units sequence passed by the request, the route length, request body and its servicing duration of every route stage. The multidimensional stationary distribution of state probabilities of the considered network is represented in the multiplicative form