Kubernetes allows to specify a session affinity for a Service: https://kubernetes.io/docs/reference/generated/kubernetes-api/v1.15/#sessionaffinityconfig-v1-core. Currently, only clientIP is supported. This makes connections from a particular client to be routed to the same backend.

The implementation of the affinity in kube-proxy is based on the recent iptables module: https://github.com/kubernetes/kubernetes/blob/v1.15.3/pkg/proxy/iptables/proxier.go#L1163.