Level‐Independent Quasi‐Birth‐and‐Death Processes

Latouche, Guy

doi:10.1002/9780470400531.eorms0461

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…As the particle is only allowed to translate to the nearest lattice sites, the problem of calculating the macrostate probabilities can be described as a quasi-birthdeath process. 52,53 In order to calculate the probabilities P(r), instead of Equation (12), we solve the global balance equation which in matrix notation can be written as…”

Section: Transition Matrix Monte Carlo Techniquementioning

confidence: 99%

Critical Casimir interactions and colloidal self-assembly in near-critical solvents

Tasios

Edison

Roij

et al. 2016

The Journal of Chemical Physics

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A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, including the pronounced fractionation of the solvent in the coexisting colloidal phases, of this complex system. We also present results for the partial structure factors; these shed light on the critical behaviour in the ternary mixture. The degree to which an effective two-body pair potential description can describe the phase behaviour and structure of the colloidal suspension is discussed briefly.

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Section: Transition Matrix Monte Carlo Techniquementioning

confidence: 99%

Critical Casimir interactions and colloidal self-assembly in near-critical solvents

Tasios

Edison

Roij

et al. 2016

The Journal of Chemical Physics

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Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

et al. 2021

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We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

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Level‐Independent Quasi‐Birth‐and‐Death Processes

Abstract: The definition and basic properties of quasi‐birth‐and‐death processes are presented, both in continuous and discrete time. The main resolution algorithms are given, and various extensions are discussed.

Cited by 2 publications

References 24 publications

Critical Casimir interactions and colloidal self-assembly in near-critical solvents

Critical Casimir interactions and colloidal self-assembly in near-critical solvents

Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

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