Delay in multihop IoT network dependent on the following source of reasons\cite{Yerra_2013}
Delay due to multi-hop
Message traverses several hops before reaching destination in multi-hop networks. Transmission power is analogous to transmission radius (r) so Low power operation of nodes in battery operated sensor networks also increases the number of hops in the network which is another reason for larger delays. Transmission power can be increased to reduce the hops but not at the cost of more interference with the neighbouring nodes.
Channel access delay
The channel access mechanisms are mostly CSMA/CA based contention access in wireless networks. Collisions creates additional exponential delays in the network. Channel access delays depends on throughput of each node, node density and number of nodes in the network and transmission power.
Aggregation and queuing delays at intermediate nodes
Aggregation and compression in adhoc networks is used to reduce the redundancy of the messages thereby reducing the channel access delays. Aggregation and compression function of throughput and protocols at intermediate nodes can lead to large delays due to processing delays before transmission. These three sources of delay are tightly coupled and should be optimized considering all the above factors. The delay experienced by a message due to network throughput, node density, silent relay nodes and transmission power is analysed using simple models to understand trade-off among them in this paper. As a result, understanding the relationship between delay and the network parameters is an important first step in providing delay differentiation.
The total end to end delay for a message to travel L units away is also derived in \cite{srieffect} as given in below equations
\[\begin{aligned} E[d_{c}]={e^{-\Lambda\tau rf^{2}}\over p}[e^{{\Lambda\pi f^{2}\over 1-{p\lambda D\over 7}}}-1],\\ f=(1+\Delta)r, \\ d_{t}=\sum_{j=1}^{n}d_{c}(j), \\ E[d_{t}]={Le^{-\Lambda\pi f^{2}}\over p \ast r}[e^{{\Lambda\pi f^{2}\over 1-{{\rm p}\lambda D\over 7}}}-1]\end{aligned}\]
The parameters considered are transmission radius (r), channel access probability (p), node density (\(\Lambda\)) and percentage of silent relay nodes (\(\alpha \))