An infinite number of nodes move in \mathbbR^2 according to a random waypoint model; a single packet is traveling towards a destination (located at an infinite distance away) using combinations of wireless transmissions and physical transport on the buffers of nodes. In earlier work [1] we defined two performance metrics, namely, the long-term average speed with which the packet travels towards its destination, and the rate with which transmission cost accumulates with distance covered. Explicit expressions were derived for these metrics, under specific ergodicity assumptions. In this paper we give a precise description of the induced Markov process, we show that it is indeed (uniformly) geometrically ergodic, and that the law of large numbers holds for the random variables of interest. In particular, we show that the two performance metrics are well-defined and asymptotically constant with probability one.
Asymptotics of the Packet Speed and Cost in a Mobile Wireless Network Model / Kontoyiannis, Ioannis; Toumpis, Stavros; Cavallari, Riccardo; Verdone, Roberto. - ELETTRONICO. - 2018-:(2018), pp. 8437523.2466-8437523.2470. (Intervento presentato al convegno 2018 IEEE International Symposium on Information Theory, ISIT 2018 tenutosi a USA nel 2018) [10.1109/ISIT.2018.8437523].
Asymptotics of the Packet Speed and Cost in a Mobile Wireless Network Model
Cavallari, Riccardo;Verdone, Roberto
2018
Abstract
An infinite number of nodes move in \mathbbR^2 according to a random waypoint model; a single packet is traveling towards a destination (located at an infinite distance away) using combinations of wireless transmissions and physical transport on the buffers of nodes. In earlier work [1] we defined two performance metrics, namely, the long-term average speed with which the packet travels towards its destination, and the rate with which transmission cost accumulates with distance covered. Explicit expressions were derived for these metrics, under specific ergodicity assumptions. In this paper we give a precise description of the induced Markov process, we show that it is indeed (uniformly) geometrically ergodic, and that the law of large numbers holds for the random variables of interest. In particular, we show that the two performance metrics are well-defined and asymptotically constant with probability one.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.