Rolling-Round-Robin Rate Overview

• Rolling-Round-Robin Rate is an umbrella term representing cyclic rate measurements across wireless, queueing, CPU scheduling, and quantum key distribution.
• In communication and scheduling systems, it quantifies effective per-user service, quota-based throughput, and rotation frequency to improve delay and performance metrics.
• In quantum key distribution, it denotes secret key rate, emphasizing cyclic pairings and measurement structures that secure quantum communications.

Searching arXiv for the exact term and closely related round-robin rate concepts across domains. “Rolling-Round-Robin Rate” is not a standard term in the arXiv literature. The closest paper-grounded interpretation is domain-dependent: in some works it denotes an effective per-user service rate induced by cyclic scheduling, in others an information transmission rate or capacity created by a round-robin mechanism, a per-round quota in packet schedulers, a dynamic time quantum that controls CPU rotation frequency, or a final secret key rate in round-robin differential phase-shift quantum key distribution. This suggests that the expression is best treated as an umbrella designation—an Editor’s term—for the rate-like quantity that emerges when service, access, assignment, or measurement proceeds in successive round-robin visits rather than through a single fixed-rate model (Yang et al., 2018, Ghassami et al., 2017, Luangsomboon et al., 2021, Behera et al., 2011, Guan et al., 2015).

1. Terminological status and scope

In the cited literature, no paper defines a metric literally called “Rolling-Round-Robin Rate.” Instead, each field instantiates a different nearest analogue. In wireless queueing, the closest quantity is the long-term per-user effective service rate under round robin, typically governed by a success probability times a scheduling fraction (Yang et al., 2018). In covert-channel analysis, the relevant object is the achievable information rate in bits per time slot induced by a round-robin scheduler (Ghassami et al., 2017). In hierarchical and deficit-based packet scheduling, the closest concept is a round-by-round quota or weighted service share that is rolled forward across rounds (Kim, 2014, Luangsomboon et al., 2021). In CPU scheduling, the closest analogue is the time quantum, because it directly controls how frequently the scheduler rotates among ready processes (Dash et al., 2016). In round-robin QKD, “rate” means secret key rate, sifted-key rate, gain, or clock rate, not scheduler throughput (Guan et al., 2015, Wang et al., 2021).

Domain	Closest quantity	Representative expression
Small-cell wireless RR	Per-user effective service rate	$\mu^\Phi_{x_0}/K_{\mathrm{s}}$ (Yang et al., 2018)
Covert queueing channel	Capacity in bits per slot	$C=\max_{0\le p\le1}\frac{h(p)}{1+p}$ (Ghassami et al., 2017)
DRR ISP traffic control	Effective excess-bandwidth share over rounds	Quantum-proportional share via $Q_i$ (Kim, 2014)
HLS packet scheduling	Per-round quota-derived service	$F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$ (Luangsomboon et al., 2021)
CPU RR variants	Rotation-controlling time quantum	$TQ=\sum BT_i/n$ or median-based $q_t$ (Dash et al., 2016, Behera et al., 2011)
RRDPS/RRDPTS QKD	Secret key rate / gain	$$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$ for RRDPTS (Wang et al., 2021)

A recurrent misconception is that round robin implies a single universal “rate.” The literature instead separates at least five different objects: access share, successful service rate, rotation frequency, information capacity, and secure key rate. Another misconception is that round robin is defined only by fairness of turn-taking. Several papers show that regularity of service opportunities, overlap structure, or quota propagation can matter as much as average share itself (Yang et al., 2018, Behrouzi-Far et al., 2022, Luangsomboon et al., 2021).

2. Wireless and queueing-theoretic service rates

In the downlink small-cell model of “Delay Analysis of Random Scheduling and Round Robin in Small Cell Networks” (Yang et al., 2018), each SAP serves $K_{\mathrm{s}}$ UEs, time is slotted, arrivals are Bernoulli with rate $\xi$, and under RR a typical UE is scheduled once every $K_{\mathrm{s}}$ slots. The paper’s closest exact analogue to a round-robin service rate is therefore the effective per-user service capability

$C=\max_{0\le p\le1}\frac{h(p)}{1+p}$0

where $C=\max_{0\le p\le1}\frac{h(p)}{1+p}$1 is the conditional wireless service success probability. This quantity governs the stability condition

$C=\max_{0\le p\le1}\frac{h(p)}{1+p}$2

the queue non-empty probability

$C=\max_{0\le p\le1}\frac{h(p)}{1+p}$3

and the mean delay

$C=\max_{0\le p\le1}\frac{h(p)}{1+p}$4

The paper further states that RR outperforms random scheduling in mean delay, with the gap

$C=\max_{0\le p\le1}\frac{h(p)}{1+p}$5

and emphasizes that the advantage is more pronounced under heavy traffic (Yang et al., 2018).

A distinct wireless interpretation appears in “Round-Robin is Provably Near-Optimal for Minimizing Age with HARQ over Heterogeneous Unreliable Multiaccess Channels” (Jiang, 2020). There, persistent round robin schedules users cyclically and persists with retransmissions until success. The cycle length is

$C=\max_{0\le p\le1}\frac{h(p)}{1+p}$6

so each user’s long-run successful update frequency is effectively $C=\max_{0\le p\le1}\frac{h(p)}{1+p}$7. Under the two HARQ models studied, the paper derives asymptotic relative AoI gap bounds of about $C=\max_{0\le p\le1}\frac{h(p)}{1+p}$8 and $C=\max_{0\le p\le1}\frac{h(p)}{1+p}$9 for RR-P under the stated conditions, showing that in this setting the “rate” of successful cyclic service can be near-optimal even when users are heterogeneous (Jiang, 2020).

3. Information, coding, and overlap-induced rates

In “A Covert Queueing Channel in Round Robin Schedulers” (Ghassami et al., 2017), the rate induced by round robin is not a service rate but an information transmission rate. The exact definition is

$Q_i$0

with units of bits per time slot. In the noiseless case the round-robin covert-channel capacity is

$Q_i$1

and with packet drops of probability $Q_i$2 it becomes

$Q_i$3

Here the round-robin mechanism itself creates the signaling alphabet, because Bob infers Alice’s bit from the pattern of his own service acknowledgments (Ghassami et al., 2017).

In “Round-Robin Streaming with Generations” (Li et al., 2012), the closest analogue is effective throughput under cyclic generation service. One coded packet from each generation is sent sequentially and then the sender wraps around. The central analytic quantity is the expected delivery packet count

$Q_i$4

where $Q_i$5 depends on how many round-robin service opportunities each generation has accumulated. The paper states that, because there is no feedback until the entire file has been downloaded, round robin may result in many superfluous transmissions for already decoded generations, but that the overhead per packet drops as generation size increases (Li et al., 2012). This is a throughput interpretation of a rolling RR rate: the file-level rate is determined by cyclic service opportunities and their induced completion distribution.

In “Balanced Nonadaptive Redundancy Scheduling” (Behrouzi-Far et al., 2022), round robin is a deterministic rolling assignment of each arriving job to $Q_i$6 consecutive servers modulo $Q_i$7. The long-run assignment frequency is perfectly balanced, expressed by

$Q_i$8

The average overlap factor is

$Q_i$9

and the overlap diversity factor is

$F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$0

The paper shows that this rolling assignment pattern can yield worse queueing performance than random despite perfect load balance, because the overlap geometry is unfavorable; the proposed block-design policy reduces average waiting time in the queue by up to $F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$1 compared to random and up to $F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$2 compared to round-robin (Behrouzi-Far et al., 2022). This suggests that a “round-robin rate” defined only by average visit frequency can miss the more consequential structure of overlap classes.

4. Packet scheduling, bandwidth allocation, and rolling quotas

In ISP traffic control, “Deficit Round-Robin-Based ISP Traffic Control Scheme Enabling Excess Bandwidth Allocation in Shared Access Networks” (Kim, 2014) associates rate with the service that accumulates over repeated DRR visits. The scheme separates conformant and non-conformant traffic using token bucket meters, serves conformant traffic first, and uses DRR for non-conformant packets. The excess-capacity target is expressed through

$F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$3

and, when $F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$4, the normalized fair rate $F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$5 satisfies

$F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$6

The scheduler itself does not output a literal rolling rate variable. Rather, service emerges from deficit counters $F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$7 and quanta $F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$8, with the intended design that quanta are proportional to token generation rates. This suggests that the nearest “rolling round-robin rate” is the effective excess-bandwidth service a subscriber accumulates over successive DRR rounds, conditional on residual capacity after conformant traffic (Kim, 2014).

In hierarchical link sharing, “A Round-Robin Packet Scheduler for Hierarchical Max-Min Fairness” (Luangsomboon et al., 2021) makes the rate interpretation even more explicit. HLS computes a fair quota

$F_i=\left\lfloor B_i/w_i^{\rm ac}\right\rfloor$9

and an active child receives quota $TQ=\sum BT_i/n$0. Unused quota is returned upward as residual and redistributed in surplus rounds. The global invariant is

$TQ=\sum BT_i/n$1

Here rate is not set by a token bucket or measured moving average; it emerges from repeated rounds, quota propagation, and residual redistribution. The paper’s transmission-gap bound,

$TQ=\sum BT_i/n$2

shows that the rolling quota process determines not only long-run allocation but also short-term revisit cadence (Luangsomboon et al., 2021).

5. CPU scheduling: quantum as round-robin rotation rate

In CPU scheduling papers, the nearest analogue to “Rolling-Round-Robin Rate” is the time quantum, because it determines how often the scheduler rotates among ready processes. “An optimized round robin cpu scheduling algorithm with dynamic time quantum” (Dash et al., 2016) states the tradeoff directly: a smaller quantum means a higher rotation rate but more context switches, while a larger quantum means a lower rotation rate and behavior closer to FCFS. Its DABRR algorithm sets

$TQ=\sum BT_i/n$3

recomputed after each round on the current ready queue. Under the paper’s six benchmark cases, DABRR reports reductions relative to standard RR of about $TQ=\sum BT_i/n$4 in waiting time and $TQ=\sum BT_i/n$5 in turnaround time (Dash et al., 2016).

“A New Proposed Dynamic Quantum with Re-Adjusted Round Robin Scheduling Algorithm and Its Performance Analysis” (Behera et al., 2011) uses the median of current burst times as the quantum: $TQ=\sum BT_i/n$6 The quantum is recalculated after each cycle using the remaining burst times, and the queue is reordered in a smallest-largest alternating pattern. This is a direct example of a rolling RR rate in the sense of a round-dependent service slice (Behera et al., 2011).

The OMDRR family makes the rolling interpretation more literal. “An Optimum Multilevel Dynamic Round Robin Scheduling Algorithm” (Goel et al., 2013) describes a round-based update

$TQ=\sum BT_i/n$7

as reconstructed from the paper’s stepwise procedure, with a small-remainder rule that allows a process to finish if its remaining burst is less than $TQ=\sum BT_i/n$8. “Simulation of an Optimum Multilevel Dynamic Round Robin Scheduling Algorithm” (Goel et al., 2013) describes an analogous multiplicative update

$TQ=\sum BT_i/n$9

together with a threshold condition based on $q_t$0 and round-by-round warping of the time slice (Goel et al., 2013). In both cases the “rate” is not throughput in the queuing sense but the amount of CPU granted per visit as the rounds progress.

A hybrid priority interpretation appears in “Characteristic specific prioritized dynamic average burst round robin scheduling for uniprocessor and multiprocessor environment” (Dash et al., 2015). There the dynamic quantum is

$q_t$1

but the order of rotation is determined by a seven-feature priority score. The paper reports, in uniprocessor experiments, reductions relative to RR of $q_t$2 in turnaround time and $q_t$3 in waiting time, and in multiprocessor experiments reductions of $q_t$4 and $q_t$5, respectively (Dash et al., 2015). At a more abstract level, “A Markov Chain Model for the Analysis of Round-Robin Scheduling Scheme” treats the nearest rate-like primitive as the forward rotation probability per quantum,

$q_t$6

with pure RR corresponding to $q_t$7 (Shukla et al., 2010).

6. Quantum key distribution: secret key rate as the round-robin rate

In QKD, round robin refers not to scheduler fairness but to random pairing of pulses in a packet. Consequently, the relevant rate is the secret key rate, or, more narrowly, the gain, sifted-key rate, and final secure throughput. “Experimental Passive Round-Robin Differential Phase-Shift Quantum Key Distribution” (Guan et al., 2015) reports a 500 MHz passive RRDPS system and states that it can generate secure key over 50 km with a bit error rate as high as 29%; the paper’s table includes a 53 km operating point with $q_t$8 and estimated phase error $q_t$9. Its asymptotic starting point is

$$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$0

and its practical post-processing formula is

$$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$1

Here “rate” is fundamentally secure-key yield under high error conditions, not a scheduling share (Guan et al., 2015).

“Experimental round-robin differential phase-shift quantum key distribution” (Li et al., 2015) presents the active-delay RRDPS variant with 128 selectable delays and reports a final key rate of 15.54 bps at total loss 18 dB and $$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$2 error rate. The packet-level rate formula is

$$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$3

where $$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$4 is the average number of valid detections per $$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$5-pulse train. In this setting, “round-robin rate” can only mean key-generation rate, because the round-robin feature is Bob’s randomized delay choice among pulse pairs (Li et al., 2015).

The most explicit rate expression appears in “Round-robin differential phase-time-shifting protocol for quantum key distribution: theory and experiment” (Wang et al., 2021). For RRDPTS, the asymptotic secret key rate is

$$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$6

with packet gain

$$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$7

The prefactor 2 reflects that each successful event yields two raw key bits. The paper reports that RRDPTS can achieve higher secret key rate than RRDPS in the condition of high quantum bit error rate, and gives proof-of-concept estimated SKRs of 1.5 kbit/s at 6 km, 1.0 kbit/s at 43 km, and 0.14 kbit/s at 80 km (Wang et al., 2021).

Across these QKD papers, a final misconception can be dispelled. The “round-robin” part of RRDPS or RRDPTS does not define a scheduler rotation rate at all; it defines a measurement structure over pulse pairs. The rate of interest is therefore cryptographic output rate. This contrasts sharply with wireless queueing, packet scheduling, and CPU scheduling, where the corresponding quantity is a service opportunity, visit frequency, or quota accumulation rate (Guan et al., 2015, Li et al., 2015, Wang et al., 2021).

Taken together, the literature shows that “Rolling-Round-Robin Rate” has no single invariant meaning. In the strongest paper-grounded sense, it names the rate-like quantity produced by repeated cyclic access: $$L\cdot R=2\bigl(Q(1-H(A|B))-e_{src}-(Q-e_{src})I_{AE}^U\bigr)$$8 in small-cell service, covert-channel capacity in bits per slot, quantum-controlled CPU rotation cadence, quota-derived packet service in DRR and HLS, or secure key rate in round-robin QKD. The exact formal object is therefore determined not by the phrase itself, but by which round-robin mechanism is rolling, what resource is being shared, and what notion of rate the underlying model treats as primary (Yang et al., 2018, Ghassami et al., 2017, Luangsomboon et al., 2021, Wang et al., 2021).