Supplementary Material to “ Dynamic Server Assignment with Task - Dependent Server Synergy ”

Let π be a nonidling fully collaborative policy. Under any fully collaborative policy, our model is equivalent to one where the service requirements of successive customers at station j ∈ {1, . . . , N} are independent and identically distributed (i.i.d.) with mean 1 αjγj , service rates of collaborating servers are additive, and the service rates depend only on servers, i.e., μij = μi for all i ∈ {1, . . . ,M}. Define Wπ,p(t) as the total work performed by time t for all servers under policy π. Then Wπ,p(t) = ∑M i=1 μit. Let Sk = ∑N j=1 Sk,j αjγj be the total service requirement of customer k for all k ≥ 1. Let Wπ = ∑Aπ(t) k=1 Sk be the total service requirement of the customers that have entered the system by time t, and Wπ,r(t) = Wπ(t)−Wπ,p(t) be the total remaining service requirement at time t for these customers. Since, E(Wπ,r(t)) ≤ N + N−1 ∑