Continuous multi-line queues and TASEP

Continuous Multi-line Queues and the Tasep

In this paper, we study a distribution Υ of labeled particles {1, 2, . . . , n} on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some (cylic) permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles i, j being next to e...

Multi-type TASEP in discrete time

The TASEP (totally asymmetric simple exclusion process) is a basic model for a one-dimensional interacting particle system with non-reversible dynamics. Despite the simplicity of the model it shows a very rich and interesting behaviour. In this paper we study some aspects of the TASEP in discrete time and compare the results to the recently obtained results for the TASEP in continuous time. In ...

Continuous feedback fluid queues

We investigate a fluid buffer which is modulated by a stochastic background process, while the momentary behavior of the background process depends on the current buffer level in a continuous way. Loosely speaking the feedback is such that the background process behaves ‘as a Markov process’ with generator at times when the buffer level is , where the entries of are continuous functions of . Mo...

Limited Processor Sharing Queues and Multi-server Queues

Cutting in Line: Social Norms in Queues

While the norm in many retail banks is to serve customers on a first-come-first-served basis, some customers try to cut the line, usually by providing an excuse for their urgency. In other queues, however, this behavior is considered unacceptable and is aggressively banned. In all of these cases, customer exhibit strategies that have not yet been explored in the operations literature: they choo...