In most urban public transit rail systems, passengers may need to make several interchanges between different lines to reach their destination. The design of coordinated timetables that enable smooth interchanges with minimal delay for all passengers is a very difficult task. This paper presents a mixed-integer-programming optimization model for this schedule synchronization problem for nonperiodic timetables that minimizes the interchange waiting times of all passengers. A novelty in our formulation is the use of binary variables that enable the correct representation of the waiting times to the “next available” train at the interchange stations. By adjusting trains' run times and station dwell times during their trips and their dispatch times, turnaround times at the terminals, and headways at the stations, our model can construct high-quality timetables that minimize transfer waiting times. We also discuss an optimization-based heuristic for the model. We have tested our algorithm for the Mass Transit Railway (MTR) system in Hong Kong, which runs six railway lines with many cross-platform interchange stations. Preliminary numerical results indicate that our approach improves the synchronization significantly compared with the current practice of using fixed headways and trip times. We also explore the trade-offs among different operational parameters and flexibility and their impact on overall passenger waiting times.

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ImportancePostradiation oral cavity squamous cell carcinoma (OCSCC) is a common secondary malignant neoplasm affecting survivors of head and neck cancer who underwent radiotherapy. The clinical, pathologic, and immune-related features of postradiation OCSCC are poorly characterized, and treatment options are limited because of surgical difficulty and high morbidity associated with reirradiation.ObjectiveTo determine whether postradiation OCSCC has distinctive clinical, pathologic, and immune-related features compared with demographic-matched sporadic OCSCC.Design, Setting, and ParticipantsThis retrospective matched cohort study was conducted at a single tertiary oncology center in Hong Kong. Participants included consecutive patients with OCSCC diagnosed between 2000 and 2020. Patients with postradiation OCSCC were matched with patients with sporadic OCSCC using age, year of diagnosis, sex, and anatomic subsites. Data analysis was performed from July to December 2022.ExposureHead and neck irradiation involving the oral cavity before the diagnosis of OCSCC.Main Outcomes and MeasuresThe primary outcomes were relapse pattern, survival, and causes of death. Pathologic features; immunohistochemical staining for programmed death–ligand 1, PD-1, MSH6, PMS2, FOXP3, and Ki67; and mRNA expression of 31 immune-related genes were also analyzed.ResultsA total of 173 patients, 60 with postradiation OCSCC (median [IQR] age, 63.8 [53.0-71.7] years; 43 men [71.7%]) and 113 with sporadic OCSCC (median [IQR] age, 64.4 [52.8-70.6] years; 83 men [73.5%]), were included. Patients with postradiation OCSCC had a higher proportion of N0 disease than those with sporadic OCSCC (50 patients [83.3%] vs 56 patients [49.6%]). With a median (IQR) follow-up of 10.2 (1.2-20.5) years, the 10-year relapse-free survival rates were lower in patients with postradiation OCSCC than sporadic OCSCC (29.6% [95% CI, 17.1%-43.2%] vs 52.4% [95% CI, 41.8%-62.0%]; P = .04), and the same was true for overall survival (30.5% [95% CI, 17.6%-44.4%] vs 52.3% [95% CI, 41.4%-62.1%]; P = .03). All relapses in patients with postradiation OCSCC were locoregional, whereas 35.2% of relapses (12 of 34 patients) in patients with sporadic OCSCC were distant. Despite similar 10-year disease-specific survival rates between the 2 groups (68.8% [95% CI, 55.8%-81.0%] vs 67.1% [95% CI, 57.5%-76.5%]; P = .91), patients with postradiation OCSCC had excess mortality due to pneumonia and cerebrovascular events. Postradiation OCSCC exhibited more adverse pathologic features (perineural invasion, worse pattern of invasion, and tumor budding), higher PD-1 expression, and higher gene expression of CD4 and TGF-β compared with sporadic OCSCC.Conclusions and RelevanceThis retrospective matched cohort study found distinctive pathologic characteristics and relapse patterns of postradiation OCSCC compared with sporadic OCSCC, which may be attributable to the lack of adjuvant radiotherapy, aggressive biologic phenotype, and different host immune response. Further exploration of the role of immune checkpoint therapy may be justified.