Q-Value, Slot Load, and Dwell Time

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

Q-Value, Slot Load, and Dwell Time

A dock-door reader expects about 48 tags in the field at once, and the chapter sizes the EPC Gen2 slot count with Q = ceil(log2(48)) = 6, giving 64 slots for the inventory round. The same pallet crosses a 2.4 m read zone at 1.2 m/s — 2.0 s of dwell time split across four antennas into 0.5 s each. This audit asks the question that Q-value choice invites: is Q a power knob that just makes reads faster, or a load-balancing knob whose wrong setting can waste the very dwell time it is meant to protect?

Companion to the chapter RFID Standards and Protocols — every number here comes from that chapter.

Ada: This chapter makes three numeric claims about a dock-door read: that Q is roughly ceil(log2(N)), that a wrong Q either collides or wastes slots, and that a moving pallet sits in the beam for only a couple of seconds. Let me put numbers on each using the chapter’s own figures – about 48 tags in the field, a 2.4 m read zone, 1.2 m/s, four antennas.

Sizing Q from a population of 48 tags, then reading each choice as a slot load N / 2^Q:

  • ceil(log2(48)) = ceil(5.5850) = 6, so Q = 6 gives 2^6 = 64 slots.
  • Load at Q = 6: 48 / 64 = 0.75 tags per slot – below one, so the population has room to spread.
  • Load at Q = 4: 2^4 = 16 slots, 48 / 16 = 3.0 tags per slot – three tags fight for every slot, so collisions dominate.
  • Load at Q = 9: 2^9 = 512 slots, 48 / 512 = 0.094 tags per slot – about 91% of slots sit empty and the reader steps through silence.

Dwell time for the moving pallet:

  • 2.4 m / 1.2 m/s = 2.0 s inside the beam.
  • Split across four antennas: 2.0 s / 4 = 0.5 s per antenna before the package geometry changes.

Payload size for a 96-bit EPC: 96 / 8 = 12 bytes of identifier, before the CRC and protocol-control bits the reader also returns.

The audit’s point is that Q is a load-balancing knob, not a power knob: keeping the slot load near one tag per slot is what lets each inventory round finish inside that half-second antenna window, so raising Q too far wastes the very dwell time it was meant to protect.

Every number above is taken from the chapter’s own material and re-derived step by step.