In broadband satellite communication systems, beam hopping (BH) is more and more welcome to compensate the low-power-efficiency wide beam and the lowspectrum-efficiency multiple spot beams simultaneously. As a flexible coverage method, BH demands efficient hopping strategy to reach the desired quality of service (QoS). In this paper, we consider the QoS equilibrium, in particular the delay fairness, among different cells illuminated by one hopping beam through designing the hopping strategy on the condition of capacity satisfaction. Due to the physical limitation that hopping speed is much slower than packet arrival speed, the ideal first-come-first-serve packet scheduling is not realizable, which compels us to pursuit the optimal slot scheduling instead. In this paper, we consider a long-term delay fairness problem by perperiod slot allocation for BH, using instantaneous and statistical information. To deal with the complex stochastic programming problem, we introduce the time-sharing principle to uncouple the variables and adopt stochastic gradient theory to deduce the suboptimal close-form solution. Our contributions are in three folds: firstly, it is the first time to consider the delay fairness not the traditional capacity fairness for BH; secondly, a general per-period decision scheme is proposed for the unique slot allocation in the perspective of queuing; thirdly, a suboptimal closeform solution for the per-period slot allocation is obtained, which could also cope with burst traffic cases. In simulation, we verify our method's advantage in terms of delay fairness comparing with the existing similar works.