FEBRUARY 2019 | VOL. 62 | NO. 2 | COMMUNICATIONS OF THE ACM 99 to the number of simultaneous sprints as each sprinter contributes to the load above rated current. Higher currents increase the probability of tripping the breaker.

Let nS denote the number of sprinters and let Ptrip denote
the probability of tripping the breaker. The breaker occupies
one of the following regions:
• Non-Tripped. Ptrip is zero when nS < Nmin
• Non-Deterministic. Ptrip is a non-decreasing function of

nS when Nmin ≤ nS < Nmax
• Tripped. Ptrip is one when nS ≥ Nmax
Note that Nmin and Nmax depend on the breaker’s trip curve and
the application’s demand for power when sprinting. For
Spark on chip multiprocessors, we find that the breaker does
and heat sink must absorb surplus heat during a sprint. 14, 15
Second, the datacenter rack must employ batteries to guard
against power emergencies caused by a surplus of sprinters
on a shared power supply. Third, the system must imple-
ment management policies that determine which chips
sprint.

2. 1. System architecture

Chip multiprocessors and thermal packages. The quality of the multiprocessor’s thermal package, measured by its thermal capacitance and conductance, determines the chip’s maximum power level and dictates the duration of a sprint. 13, 15 More expensive heat sinks employ PCMs, which increase thermal capacitance, and permit sprint durations on the order of minutes if not hours. We estimate a chip with paraffin wax can sprint with durations on the order of 150s.

After a sprint, the thermal package must release its heat before the chip can sprint again. The average cooling duration, denoted as ∆tcool, is the time required before the PCM returns to ambient temperature. The rate at which the PCM dissipates heat depends on its melting point and the thermal resistance between the material and the ambient. Both factors can be engineered and, with paraffin wax, we estimate a cooling duration on the order of 300s, twice the sprint’s duration.

Power delivery and circuit breakers. Datacenter architects deploy servers and multiprocessors to oversubscribe power distribution units for efficiency. Oversubscription utilizes a larger fraction of the facility’s provisioned power. But it relies on power capping and varied computational load across servers to avoid tripping circuit breakers or violating contracts with utility providers. 4 Although sprints can boost computation, the risk of a power emergency increases with the number of sprinters in a power capped datacenter.

Figure 2 presents the circuit breaker’s trip curve, which specifies how sprint duration and power combine to determine whether the breaker trips. The trip time corresponds to the sprint’s duration. Longer sprints increase the probability of tripping the breaker. The current draw corresponds

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Figure 1. Normalized speedup, power, and temperature for varied Spark benchmarks when sprinting. Nominal operation supplies three cores at 1.2GHz. Sprint supplies twelve cores at 2.7GHz.

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Figure 2. Typical trip curve of a circuit breaker. 5