Upper bounds for the min–max and min–sum cost online problems in wireless ad hoc networks

A sequence of online messages for connections is given, each message is important and thide failure of delivering a message is a critical event. The maximum lifetime problem maximizes the total number of messages that can be successfully sent over the network. Given a \(h\ge 1\), this paper presents two new problems on ad hoc networks (called the min–max and min–sum cost online problems), which adjust the initial energies of nodes such that the network can send the first \(h\) messages. We consider the min–sum and min–max norms for minimizing the cost of adjusting the initial energies. This paper presents an algorithm for these problems and computes upper bounds for the total cost of the min–sum and min–max norms. Mohanoor et al. (Ad hoc Networks 7: 918–931, 2009) presented three algorithms (called SWRP, SFWP and SWCRP algorithms) to online energy aware routing, which, in practice, are better than other algorithms on lifetime in the cases: the effect of session length, transmission radius and node density. This paper modifies these algorithms (the modifies algorithms are called TSWRP, TSFWP and TSWCRP) so that they compute the total cost of the min–sum and min–max norms. Then, we show, in practice, the total cost of the min–sum and min–max norms computed by our algorithm are smaller than the values computed by the TSWRP, TSFWP and TSWCRP algorithms in the cases: the transmission radius and node density. Also, in practice, the lifetime of our algorithm is more than the lifetime of the SWRP, SFWP and SWCRP algorithms in the cases: the effect of session length and node density.