To address an important care issue in Canada, we tested the association between paramedic system hospital offload and response time, while considering the impact of other system-level factors. Data from Calgary, Alberta (2014-2017), included median offload (exposure) and response (outcome) time aggregated by hour, with covariates paramedic system episodes of care-dispatch and arrival of a response unit-and hospital transport arrivals (collectively called volume), time of day, and season. Analyses used linear regression and modified Poisson models. 301,105 EMS episodes of care over 26,193 1-h periods were included. For any given 1-h period, the median (IQR) across all episodes of care for offload time, response time, episodes of care, and hospital transport arrivals were 55.3 (45.7, 66.3) min, 8.6 (7.6, 9.8) min, 12 (8, 16) episodes, and 8 (5, 10) hospital arrivals, respectively. Multivariable modelling revealed a complex association differing over levels of exposure and covariates, requiring description using "light stress" and "heavy stress" system scenarios. The light scenario was defined as median offload of 30 min and volume < 10th percentile (six episodes and four hospital arrivals), in the summer, and the heavy scenario as median offload of 90 min and volume > 90th percentile (17 episodes and 13 hospital arrivals), in the winter. An increase is reported in minutes:seconds for median hourly response time between scenarios by time of day: 1:04-4:16 (0000-0559 h.), 0:42-2:05 (0600-1159 h.), 0:57-3:01 (1200-1759 h.), and 0:18-2:21 (1800-2359 h.). Increasing offload is associated with increased response time; however the relationship is complex, with a greater impact on response time noted in select situations such as high volume in the winter. These observations illustrate the interdependence of paramedic, ED, and inpatient systems and provide high-yield targets for polices to mitigate the risk to community availability of paramedic resources at times of high offload delay/system stress.