S M Nazmuz Sakib Delivery-Normalized Inflow Principle and Sakib Number for Jackson Queue Networks Applied to Food Supply Chains

We develop a delivery-normalized resource metric (the Sakib Number) for open Jacksonlike queue networks (JQN) representing food supply chains with losses. Let R denote upstream resource inflow (e.g., water embedded in primary production) and let D be the mass delivered to end users. We define the Sakib Number S := R/D and show it equals the inverse of the end-to-end survival probability in a serial chain, and more generally a renewal-reward-type ratio in a network with returns and side streams. We derive sensitivity formulae linking marginal changes in stage losses to S using absorbing Markov chain fundamentals and fractional programming arguments. Using real data from APHLIS for Kenya maize (2021) and UNEP's 2024 Food Waste Index, we compute data-based figures that (i) decompose stagewise loss, (ii) quantify the gap between naive intensity accounting and delivery-normalized accounting, and (iii) trace intervention priorities. To our knowledge, the specific normalization as a network-level invariant with closed-form sensitivity through the fundamental matrix, positioned for JQN-style analysis, has not been presented in queueing or food-systems literature. We discuss novelty, limitations, and publication readiness.