This article, working within the ‘infrastructural turn’, combines social reproduction and Lefebvrian rhythm analysis to examine the everyday labour and life of migrant cleaners and delivery service gig workers in Stockholm. Using in-depth interviews, we demonstrate how this highly mobile and flexible workforce makes the city ‘tick’ by keeping its inhabitants clean, fed, healthy and cared for. Specifically, we highlight a contradiction: workers extricating free time for others through reproductive labour, are themselves systematically deprived of the (paid and unpaid) time necessary to meet their own reproductive needs. The conditions of work in the urban on-demand and just-in-time service economy, we show, produce spatiotemporal (dis)orders of living and labouring in the algorhythmic city, as workers are required to be both on standby, waiting, whilst also fulfilling customer orders at an ever-increasing speed. Migrant gig workers who appear on the doorstep, on demand and just in time, form a kind of human infrastructure, serving the urban population whilst nonetheless being subject to disinvestment – unrepaired and unmaintained. This article, then, contributes to the literature on gig work, migration and social reproduction, by theorizing the algorhythmic city as reliant on the constant transformation of gig labour into an urban infrastructure for social reproduction.