Q-Value, Slot Load, and Dwell Time
Q-Value, Slot Load, and Dwell Time
Ada re-derives this chapter’s own numbers step by step, at full precision
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.
See the relationship before changing it
The figure reads from left to right. The blue card is tags in the field. The middle card applies this page's rule. The green card is slot load at q=6. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only tags in the field, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 48 tags.
- 2
Name the relationship. slot load = tags / 2^6 slots
- 3
Substitute with units. 48 / 64 = 0.75 tags/slot
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change tags in the field
Try Predict the direction of slot load = tags / 2^6 slots. Test another tags in the field, then compare slot load at q=6.
Observe Population, not transmit power, sets contention against the fixed sixty-four-slot round. Reset tags in the field to 48 and compare slot load at q=6.
Explain Population, not transmit power, sets contention against the fixed sixty-four-slot round.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Treat 48 tags and Q = 6, yielding 64 slots, as the fixed audit case; predict the collision result before using Check audit.
The slot-load indicator shows 0.75 tag/slot; at Q = 9 it drops near 0.094 and empty-slot waste rises sharply.
Q balances contention because slot count grows as 2^Q: too few slots collide, while too many consume the 0.5 s antenna dwell in silence.
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, soQ = 6gives2^6 = 64slots.- Load at
Q = 6:48 / 64 = 0.75tags per slot – below one, so the population has room to spread. - Load at
Q = 4:2^4 = 16slots,48 / 16 = 3.0tags per slot – three tags fight for every slot, so collisions dominate. - Load at
Q = 9:2^9 = 512slots,48 / 512 = 0.094tags 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 sinside the beam.- Split across four antennas:
2.0 s / 4 = 0.5 sper 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.
Technical boundaries: This occupancy ratio excludes Gen2 slot-duration details, capture effect, retransmissions, heterogeneous tag response times, RF misses, and reader adaptation of Q during a round.