  Quantum networks will be able to service consumers with long-distance
entanglement by use of quantum repeaters that generate Bell pairs (or links)
with their neighbors, iid with probability $p$ and perform Bell State
Measurements (BSMs) on the links that succeed iid with probability $q$. While
global link state knowledge is required to maximize the rate of entanglement
generation between any two consumers, it increases the protocol latency due to
the classical communication requirements and requires long quantum memory
coherence times. We propose two entanglement routing protocols that require
only local link state knowledge to relax the quantum memory coherence time
requirements and reduce the protocol latency. These protocols utilize
multi-path routing protocol and time multiplexed repeaters. The time
multiplexed repeaters first generate links for $k$-time steps before performing
BSMs on any pairs of links. Our two protocols differ in the decision rule used
for performing BSMs at the repeater: the first being a static path based
routing protocol and second a dynamic distance based routing protocol. The
performance of these protocols depends on the quantum network topology and the
consumers' location. We observe that the average entanglement rate and the
latency increase with the time multiplexing block length, $k$, irrespective of
the protocol. When a step function memory decoherence model is introduced such
that qubits are held in the quantum memory for an exponentially distributed
time with mean $\mu$, an optimal $k$ ($k_\text{opt}$) value appears, such that
for increasing $k$ beyond $k_{\rm opt}$ hurts the entanglement rate. $k_{\rm
opt}$ decreases with $p$ and increases with $\mu$. $k_{\rm opt}$ appears due to
the tradeoff between benefits from time multiplexing and the increased
likelihood of previously established Bell pairs decohering due to finite memory
coherence times.
