Corollary 2.4 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].sub.m], conditioned on the event that W = UV is decomposable with U and V of the same length (and type) as u and v, respectively.
As an example, consider the TASEP on [[OMEGA].sub.(1,1,1,1)] with n = 4 and [t.sub.1] = [t.sub.2] = [t.sub.3] = [t.sub.4] = 1.
= [t.sub.r] and discovered that the TASEP on a ring is a projection of a richer process involving combinatorial structures called multi-line queues.
Theorem 3.1 The stationary distribution [pi] of the TASEP on [[OMEGA].sub.m] with inverse rates [t.sub.1], ..., [t.sub.r] is given by [pi](w) = [w]/[Z.sub.m].
 Erik Aas, Stationary probability of the identity for the TASEP on a ring, arXiv:1212.6366
 Chikashi Arita and Kirone Mallick: Matrix product solution to an inhomogenous multi-species TASEP. arXiv:1209.1913
 Arvind Ayyer and Svante Linusson, An inhomogenous multispecies TASEP on a ring.
 Svante Linusson and James Martin, Stationary probabilities for an inhomogeneous multi-type TASEP, in preparation.
In this Section, we first derive expressions for per-hop success probability with different hopping strategies using stochastic geometry, and then combine with TASEP model to derive the performance metric of the spatial density of transport and the average end-to-end delay.
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.
Haenggi, "The TASEP: A Statistical Mechanics Tool to Study the Performance of Wireless Line Networks," in Proc.