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REVIEW 5 major objections 5 minor 31 references

Redundancy Scheduling in Systems with Bi-Modal Job Service Time Distribution

T0 review · 5 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A non-adaptive, stateless scheduler based on balanced incomplete block designs gives perfect load balance and the best overlap diversity in the urns-and-balls model, and simulations show it reduces queueing time for bi-modal workloads…

desk verdict BIBD scheduling is a neat idea with plausible simulation support, but the queueing claim rests on an explicitly unproved analogy and a thin set of experiments. read the letter →

arxiv 1908.02415 v2 pith:5LA26LFN submitted 2019-08-07 cs.PF cs.DCcs.ITmath.IT

Amir Behrouzi-Far , Emina Soljanin This is my paper · ORCID
classification cs.PFcs.DCcs.ITmath.IT MSC 05B0560K2568M20
keywords redundancyschedulingbi-modaljobsizesbalancedincompleteblockdesignsnon-adaptivequeueingtimeloadbalancingurnsandballsoverlapdiversity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper studies a distributed system where each arriving job is replicated to $r$ of $n$ servers and the losing copies are cancelled as soon as one copy starts service, with job sizes drawn from a bi-modal distribution of short or long exponential service times. It argues that for such workloads a scheduler must balance two things: spreading load evenly and diversifying the set of servers chosen for successive jobs so a short job is not trapped behind a long job in every queue it joins. To compare policies, the paper maps the arrival process to an urns-and-balls model and defines three indicators: the load balancing factor (LBF), redundancy overlap factor (ROF), and redundancy diversity factor (RDF). It claims that a policy based on balanced incomplete block designs (BIBD) achieves perfect load balancing and the best diversity of redundancy among the three non-adaptive policies studied, and that simulations show it reduces average queueing time relative to random and round-robin scheduling. If true, this gives a simple, stateless scheduling rule that improves latency in systems with two-speed jobs without inspecting queue lengths.

What carries the argument

The central object is the symmetric balanced incomplete block design with $\lambda=1$, written $(n,r,1)$-BIBD: a collection of $n$ blocks, each of size $r$, over $n$ server labels such that every pair of labels appears together in exactly one block. The scheduler picks blocks cyclically, one per arriving job. The supporting machinery is the urns-and-balls analogy, in which $T$ arrivals place one ball in each of $r$ chosen urns, and the three indicators $LBF$, $ROF$, and $RDF$ defined from urn occupancies and overlap counts; the paper derives these indicators for each policy and uses their ranking to predict queueing performance.

What would settle it

Run the same queueing simulation with the long-job probability $p$ set to 0 or with $q=1$, so the service-time distribution is effectively exponential and bi-modality disappears; if BIBD no longer beats random and round-robin, the claimed benefit is driven by bimodality as the paper's mechanism asserts. Independently, record the empirical distribution of overlaps between the $r$-server sets assigned to consecutive jobs in the full queueing simulation and compare its first two moments with the paper's $ROF$ and $RDF$ formulas; disagreement would show the arrival-only indicators miss queue-dependent effects.

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Extended reading notes

Core claim

The paper claims that, for a system of $n$ identical servers where each job is replicated to $r$ servers and extra copies are cancelled as soon as one copy enters service, the scheduling rule should be judged by two urns-and-balls indicators: load balance and overlap diversity. It proposes using the blocks of a symmetric $(n,r,1)$-BIBD, cycled in round-robin order, so that every pair of servers appears together in exactly one block and consecutive jobs share almost no servers. For $n = r(r-1)+1$, the paper derives closed-form values of $LBF$, $ROF$, and $RDF$ for random, round-robin, and BIBD scheduling: BIBD matches random on overlap diversity while reaching the perfect load balance of round-robin, and round-robin has strictly worse diversity. On this basis it concludes that BIBD provides perfect load balancing and the best performance in terms of diversity of redundancy among the three non-adaptive policies. Simulated queueing times then show BIBD below both alternatives across arrival rates, with the largest gains when long jobs are rare but very slow.

Load-bearing premise

The paper's queueing conclusions rest on the stated belief that a policy's load-balance and overlap-diversity indicators in an arrival-only urns-and-balls model predict its queueing time in the real system; if that analogy fails, the simulated advantages are not backed by the analysis.

Editorial extensions

If this is right

  • A stateless scheduler can reduce average queueing time for bi-modal workloads without inspecting queue lengths or server loads, as long as it balances loads and controls overlap between consecutive jobs' server sets.
  • BIBD scheduling inherits round-robin's perfect load balance when $n \mid T$ and random scheduling's overlap diversity, so it does not have to trade one objective for the other.
  • Round-robin's weakness is not load balancing but overlap diversity: its $RDF$ is strictly smaller than BIBD's and shrinks as $r$ grows, predicting larger queueing losses at high redundancy.
  • The simulations show larger BIBD gains when long jobs are rare but slow, meaning the policy is most valuable in exactly the skewed bi-modal regimes observed in real cluster workloads.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because $(n,r,1)$-BIBDs exist only for $n = r(r-1)+1$, practical deployment would need near-balanced or other design families; testing whether the indicators degrade gracefully when the exact balance condition is relaxed is a natural next step.
  • The analogy's validity can be probed by measuring the actual overlap distribution inside the full queueing simulation and checking whether the first two moments track the paper's $ROF$ and $RDF$ formulas across different loads.
  • The same LBF/ROF/RDF indicators could also rank adaptive policies against BIBD, offering a common language for comparing stateless and stateful schedulers on bi-modal workloads.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper studies non-adaptive redundancy scheduling in a system of n servers with bi-modal job service times. It develops an urns-and-balls analogy and defines three performance indicators (LBF, ROF, RDF), evaluates random and round-robin policies in that model, proposes a scheduling policy based on symmetric balanced incomplete block designs (BIBDs), and reports simulation results which indicate that the BIBD policy reduces mean queueing time compared with random and round-robin scheduling. The paper's central assertion is that the BIBD policy combines perfect load balancing with good diversity of redundancy and therefore outperforms the two classical non-adaptive policies.

Significance. If the heuristic analogy is accepted, the paper offers a simple, elegant non-adaptive policy with closed-form indicator values and demonstrates potentially large queueing-time gains in simulation. The indicator definitions are parameter-free, no constants are fitted to the simulation data, and the BIBD construction is a clean combinatorial idea with exact load balancing by design. The paper also makes the useful observation that round-robin scheduling, despite perfect average load balance, is poor at diversifying the server sets of consecutive jobs. The main limitation is that the analytical bridge from the urns-and-balls indicators to actual queueing delay is explicitly stated only as a belief, and the validating simulations cover just two BIBD instances. The current manuscript is therefore best read as a promising heuristic plus a narrow simulation study rather than a proven scheduling result.

major comments (5)
  1. [Section III-A] The entire analytical comparison rests on the sentence 'We believe that a scheduling policy's capability of improving these indicators in the only-arrival system is a good indicator of its performance in the actual queuing system.' No theorem or formal scaling argument connects LBF/ROF/RDF to mean queueing time, and the indicators ignore the service-time realization, the cancellation dynamics, and the fact that a job waits only when all r selected servers are busy. A further load-bearing issue is that LBF in Definition 1 depends on an unspecified horizon T; for fixed n and r, the random-policy LBF in Lemma 1 tends to 1 as T grows, so the finite-horizon LBF advantage of BIBD over random disappears in the limit. The authors should either prove a formal connection (e.g., in a heavy-traffic or asymptotic regime) or substantially expand the simulation evidence, including a sweep of p, q, utilization, n, and r, to establish the analogy empirically.
  2. [Section III-C, Proposition 1] The formulas ROF_rand = n/r^2 and RDF_rand = n(n-1)/(r^2(n+r(r-2))) in Proposition 1 are stated with 'The proof is omitted because of the space constraint.' These formulas are load-bearing because Table I uses them to conclude that random has the same ROF as round-robin/BIBD and the same RDF as BIBD. An omitted proof is not acceptable for a core analytical result; please provide a full proof or an explicit reference that contains it.
  3. [Section III-F and Table I] The text claims that BIBD 'has the best performance in terms of diversity of redundancy,' but this is contradicted by Table I: RDF_BIBD = RDF_random = ((r-1)^2+r)/(r(2r-1)), and all three policies have the identical ROF. The only indicator on which BIBD strictly exceeds random is LBF. Thus the paper's own indicators attribute BIBD's queueing-time advantage over random to load balancing, not diversity. The narrative should be corrected to match the table, or a different notion of diversity should be defined and justified.
  4. [Section III-E2] The paper notes that a (n,r,1)-BIBD is not possible for arbitrary parameters but does not state the concrete restriction: a symmetric (n,r,1)-BIBD is a projective plane of order r-1, known to exist for prime-power orders and not known to exist in general, with order 6 (r=7) known to be impossible. Since n = r(r-1)+1 is necessary but not sufficient, the proposed policy is unavailable for many values of r, and the simulations only instantiate r=4 and r=5. This restriction should be stated explicitly, and its practical impact on the claimed general superiority of BIBD scheduling should be discussed.
  5. [Section IV] The queueing-time claim rests entirely on the simulations, but the simulation study is narrow: only (n,r) = (13,4) and (21,5), four (q,p) settings, and no information about run length, number of independent replications, warm-up period, or statistical error. The reported improvements of 10-20% could be within simulation noise. Please add confidence intervals or error bars, report full experimental details, and ideally sweep the arrival rate, p, q, and the available (n,r) combinations.
minor comments (5)
  1. [Section III-B] In Definition 1, the order statistics N^T_{1:n} and N^T_{n:n} should be explicitly identified as the minimum and maximum occupancy; currently the notation is introduced only verbally.
  2. [Section III-C] The use of 'max{0,...}' inside the asymptotic limit in equation (5) is informal; a statement about finite-n approximations with error bounds would be clearer.
  3. [Section IV] The captions of Figures 5-8 do not state which subfigure corresponds to low versus high arrival rate; please label the subfigures or clarify in the captions.
  4. [General] There are several typos and stylistic issues: 'experiment1' should be 'experiment 1'; 'when jobs' service time are is bi-modal'; 'distributions..'; and 'it's performance' in Section III-A should be 'its performance'.
  5. [Section IV] The simulation section does not state whether the simulator code or seeds are available; for a simulation-based central claim, a reproducibility statement would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: BIBD is deliberately designed to optimize the paper's own indicators, but the queueing-time claim rests on independent simulations, not on the indicator definitions.

full rationale

The derivation chain does not reduce to its own inputs. The urns-and-balls indicators LBF/ROF/RDF are defined independently of the queueing metric, and the values for random, round-robin, and BIBD are derived from the policies' combinatorial properties rather than fitted to queueing data. BIBD is deliberately constructed to balance loads (by cycling through blocks) and to minimize pairwise overlap (via lambda=1), so the favorable indicator values follow from that design choice; this is construction, not circular prediction. The central queueing-time claim is not derived from the indicators alone: Section IV tests the policies by explicit simulation under four parameter tuples, and the paper itself marks the indicator-to-delay connection as a belief in Section III-A ('We believe that a scheduling policy's capability of improving these indicators in the only-arrival system is a good indicator of it's performance in the actual queuing system'). That is an acknowledged, unproved heuristic and an evidentiary limitation, not a circular step. The only self-citation used in an analytical step is [29] for the asymptotic random-LBF formula in Lemma 1; this is a peripheral supporting calculation, not a load-bearing uniqueness argument or a renamed prediction. No fitted parameters are presented as predictions, and no result is imported from the authors' prior work to forbid alternatives. The paper's main weakness is the gap between the proxy indicators and actual queueing delay, plus the small number of simulated BIBD instances; those are validation concerns, not circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No fitted parameters appear in the paper. The analytical load is carried by the unproved urns-to-queueing analogy, by asymptotic balls-and-bins approximations cited from prior work, and by the existence of symmetric BIBDs. The simulations provide independent evidence, but only for four parameter tuples and without error analysis.

assumptions (4)
  • domain assumption Only-arrival urns-and-balls indicators (LBF, ROF, RDF) predict queueing time of the real system.
    Section III-A states "We believe..." and no proof is given; all analytical comparisons and the motivation for BIBD scheduling depend on this bridge.
  • standard math The asymptotic maximum and minimum loaded urn formulas from [28] and [29] approximate finite-n, finite-T random scheduling.
    Lemma 1 in Section III-C applies limit n to infinity results, Equations (6) through (9), to finite n and T in Table I and Figure 4.
  • domain assumption A symmetric (n,r,1)-BIBD exists whenever n = r(r-1) + 1.
    Section III-E says "For that to exist, n and r should satisfy n = r(r-1)+1." This condition is necessary but not sufficient; projective planes of order r-1 do not exist for all orders, so the policy is not universally applicable.
  • domain assumption Bi-modal service-time model: short jobs are exponential with rate mu1, long jobs are exponential with rate mu1/q, job type probability is p, and each copy samples the job's service-time distribution.
    Section II-A introduces this model, motivated by Google traces, but the analysis and simulations only cover this model and not heavy-tailed service-time distributions.

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Pith. "Pith review of Redundancy Scheduling in Systems with Bi-Modal Job Service Time Distribution." pith.science (2026). https://pith.science/paper/5LA26LFN

@misc{pith2026190802415,
  author       = {Pith},
  title        = {Pith review of: Redundancy Scheduling in Systems with Bi-Modal Job Service Time Distribution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5LA26LFN}},
  note         = {Machine review of arXiv:1908.02415}
}
read the original abstract

Queuing systems with redundant requests have drawn great attention because of their promise to reduce the job completion time and variability. Despite a large body of work on the topic, we are still far from fully understanding the benefits of redundancy in practice. We here take one step towards practical systems by studying queuing systems with bi-modal job service time distribution. Such distributions have been observed in practice, as can be seen in, e.g., Google cluster traces. We develop an analogy to a classical urns and balls problem, and use it to study the queuing time performance of two non-adaptive classical scheduling policies: random and round-robin. We introduce new performance indicators in the analogous model, and argue that they are good predictors of the queuing time in non-adaptive scheduling policies. We then propose a non-adaptive scheduling policy that is based on combinatorial designs, and show that it has better performance indicators. Simulations confirm that the proposed scheduling policy, as the performance indicators suggest, reduces the queuing times compared to random and round-robin scheduling.

Figures

Figures reproduced from arXiv: 1908.02415 by the authors.

Figure 1
Figure 1. System model. for each arriving job r servers are randomly selected and one copy gets assigned to each server. Round-robin policy on the other hand takes a more structured approach, where it assigns jth copy of ith arriving job to the server indexed by ((i − 1)r + j) mod n for j = 1, 2, . . . , r. We then propose a new scheduling policy based on combinatorial block designs, which is also a non-adaptive policy, and s… view at source ↗
Figure 2
Figure 2. Average number of balls in the maximum and the minimum loaded [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Load balancing factor (LBF) after 50 repetitions of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: LBF and RDF for non-adaptive scheduling policies as a function [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: Average queuing time for non-adaptive scheduling policies, with [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 5
Figure 5. Figure 5: Average queuing time for non-adaptive scheduling policies, with [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 8
Figure 8. Figure 8: Average queuing time for non-adaptive scheduling policies, with [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

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