4 Let u[upsilon] be a decomposable word of type m and let W be a random word sampled from the stationary distribution of the TASEP on [[OMEGA].
r] and discovered that the TASEP on a ring is a projection of a richer process involving combinatorial structures called multi-line queues.
1 The stationary distribution [pi] of the TASEP on [[OMEGA].
1] Erik Aas, Stationary probability of the identity for the TASEP on a ring, arXiv:1212.
3] Chikashi Arita and Kirone Mallick: Matrix product solution to an inhomogenous multi-species TASEP.
4] Arvind Ayyer and Svante Linusson, An inhomogenous multispecies TASEP on a ring.
9] Svante Linusson and James Martin, Stationary probabilities for an inhomogeneous multi-type TASEP, in preparation.
Proof: As the MAC protocol assumed for each flow is slotted ALOHA, the TASEP model of parallel type can be used for our analysis .
Using concepts and tools from the stochastic geometry and TASEP model, closed-form expressions of two main end-to-end performance metrics, the spatial capacity density and the average end-to-end delay, are derived.