Elastic Optical Networks (EONs) have the potential to improve the fiber spectrum utilization by allocating spectrum resources to multiple traffic requests proportionally to the amount of carried traffic. However, achieving high spectrum utilization in this elastic scenario is hindered by the resulting spectrum fragmentation. A number of studies have addressed and made attempts to mitigate spectrum fragmentation. Most of these studies are based on simulation techniques and target the overall blocking probability experienced by the offered traffic requests due to the lack of available spectrum resources. Some studies have also shown that blocking probability in EON can be uneven, i.e., high-rate circuit requests are more likely to be blocked when compared to low-rate requests due to the shortage of contiguously available spectrum resources. The contribution of this paper is to extend an existing Markov Chain (MC) model previously proposed by the authors to quantify blocking probability in a two-service elastic fiber link. The model extension accounts for a self-limited and partial sharing of the fiber spectrum to accommodate the two types of service. The MC model is used to quantify both the blocking probability and its fairness across the two types of service, documenting how the EON uneven blocking behavior can be significantly mitigated by performing partial (as opposed to full) sharing of the fiber spectrum.