Stochastic network calculus is the probabilistic extension of deterministic network calculus for offering stochastic performance guarantee in packet networks. However, it has been shown that the attempts to achieve a scalable stochastic performance bound only have limited success. In this paper, we propose a stochastic network calculus approach to perform scalability analysis for end-to-end delay. With statistical independence assumptions on arrival and services across multiple network nodes, we present a linear delay bound with its moment generating functions. For further improving the scalability of the bound, the tightness of the bound is investigated using Doob's maximal inequality on a suitable martingale construction. Numerical results validate that our solution improve the scalability of stochastic delay bound in terms of the linear scaling and tightness. The results are applicable to general computer network to determine a path that meets the delay requirements.