Time division multiple access (TDMA) based medium access control (MAC) protocols can provide QoS with guaranteed access to the wireless channel. However, in multi-hop wireless networks, these protocols may introduce scheduling delay if, on the same path, an outbound link on a router is scheduled to transmit before an inbound link on that router. The total scheduling delay can be quite large since it accumulates at every hop on a path. This paper presents a method that finds conflict-free TDMA schedules with minimum scheduling delay. We show that the scheduling delay can be interpreted as a cost, in terms of transmission order of the links, collected over a cycle in the conflict graph. We use this observation to formulate an optimization, which finds a transmission order with the min-max delay across a set of multiple paths. The min-max delay optimization is NP-complete since the transmission order of links is a vector of binary integer variables. We devise an algorithm that finds the transmission order with the minimum delay on overlay tree topologies and use it with a modified Bellman-Ford algorithm, to find minimum delay schedules in polynomial time. The simulation results in 802.16 mesh networks confirm that the proposed algorithm can find effective min-max delay schedules.
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