diff --git a/yarn-project/circuit-types/src/interfaces/server_circuit_prover.ts b/yarn-project/circuit-types/src/interfaces/server_circuit_prover.ts
index 69c096cca47..40e4e01f33c 100644
--- a/yarn-project/circuit-types/src/interfaces/server_circuit_prover.ts
+++ b/yarn-project/circuit-types/src/interfaces/server_circuit_prover.ts
@@ -37,6 +37,7 @@ export interface ServerCircuitProver {
   getBaseParityProof(
     inputs: BaseParityInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<RootParityInput<typeof RECURSIVE_PROOF_LENGTH>>;
 
   /**
@@ -46,6 +47,7 @@ export interface ServerCircuitProver {
   getRootParityProof(
     inputs: RootParityInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<RootParityInput<typeof NESTED_RECURSIVE_PROOF_LENGTH>>;
 
   /**
@@ -55,6 +57,7 @@ export interface ServerCircuitProver {
   getBaseRollupProof(
     baseRollupInput: BaseRollupInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<BaseOrMergeRollupPublicInputs>>;
 
   /**
@@ -64,6 +67,7 @@ export interface ServerCircuitProver {
   getTubeProof(
     tubeInput: TubeInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<{ tubeVK: VerificationKeyData; tubeProof: RecursiveProof<typeof RECURSIVE_PROOF_LENGTH> }>;
 
   /**
@@ -73,6 +77,7 @@ export interface ServerCircuitProver {
   getMergeRollupProof(
     input: MergeRollupInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<BaseOrMergeRollupPublicInputs>>;
 
   /**
@@ -82,6 +87,7 @@ export interface ServerCircuitProver {
   getRootRollupProof(
     input: RootRollupInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<RootRollupPublicInputs>>;
 
   /**
@@ -91,6 +97,7 @@ export interface ServerCircuitProver {
   getPublicKernelProof(
     kernelRequest: PublicKernelNonTailRequest,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<PublicKernelCircuitPublicInputs>>;
 
   /**
@@ -100,23 +107,26 @@ export interface ServerCircuitProver {
   getPublicTailProof(
     kernelRequest: PublicKernelTailRequest,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<KernelCircuitPublicInputs>>;
 
   getEmptyPrivateKernelProof(
     inputs: PrivateKernelEmptyInputData,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<KernelCircuitPublicInputs>>;
 
   getEmptyTubeProof(
     inputs: PrivateKernelEmptyInputData,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndTubeProof<KernelCircuitPublicInputs>>;
 
   /**
    * Create a proof for the AVM circuit.
    * @param inputs - Inputs to the AVM circuit.
    */
-  getAvmProof(inputs: AvmCircuitInputs, signal?: AbortSignal): Promise<ProofAndVerificationKey>;
+  getAvmProof(inputs: AvmCircuitInputs, signal?: AbortSignal, epochNumber?: number): Promise<ProofAndVerificationKey>;
 }
 
 /**
diff --git a/yarn-project/circuit-types/src/l2_block_downloader/l2_block_downloader.ts b/yarn-project/circuit-types/src/l2_block_downloader/l2_block_downloader.ts
index 8c43ce23925..ce4e2eb5f67 100644
--- a/yarn-project/circuit-types/src/l2_block_downloader/l2_block_downloader.ts
+++ b/yarn-project/circuit-types/src/l2_block_downloader/l2_block_downloader.ts
@@ -1,6 +1,6 @@
 import { INITIAL_L2_BLOCK_NUM } from '@aztec/circuits.js/constants';
-import { MemoryFifo, Semaphore, SerialQueue } from '@aztec/foundation/fifo';
 import { createDebugLogger } from '@aztec/foundation/log';
+import { FifoMemoryQueue, Semaphore, SerialQueue } from '@aztec/foundation/queue';
 import { InterruptibleSleep } from '@aztec/foundation/sleep';
 
 import { type L2Block } from '../l2_block.js';
@@ -21,7 +21,7 @@ export class L2BlockDownloader {
   private interruptibleSleep = new InterruptibleSleep();
   private readonly semaphore: Semaphore;
   private readonly jobQueue = new SerialQueue();
-  private readonly blockQueue = new MemoryFifo<L2Block[]>();
+  private readonly blockQueue = new FifoMemoryQueue<L2Block[]>();
   private readonly proven: boolean;
   private readonly pollIntervalMS: number;
 
diff --git a/yarn-project/foundation/package.json b/yarn-project/foundation/package.json
index 9940003d2f5..cc7b6512aef 100644
--- a/yarn-project/foundation/package.json
+++ b/yarn-project/foundation/package.json
@@ -17,7 +17,7 @@
     "./crypto": "./dest/crypto/index.js",
     "./error": "./dest/error/index.js",
     "./eth-address": "./dest/eth-address/index.js",
-    "./fifo": "./dest/fifo/index.js",
+    "./queue": "./dest/queue/index.js",
     "./fs": "./dest/fs/index.js",
     "./hash": "./dest/hash/index.js",
     "./json-rpc": "./dest/json-rpc/index.js",
diff --git a/yarn-project/foundation/src/index.ts b/yarn-project/foundation/src/index.ts
index 0f662455cab..a422558dd66 100644
--- a/yarn-project/foundation/src/index.ts
+++ b/yarn-project/foundation/src/index.ts
@@ -9,7 +9,7 @@ export * as crypto from './crypto/index.js';
 export * as errors from './error/index.js';
 export * as ethAddress from './eth-address/index.js';
 export * as fields from './fields/index.js';
-export * as fifo from './fifo/index.js';
+export * as fifo from './queue/index.js';
 export * as fs from './fs/index.js';
 export * as jsonRpc from './json-rpc/index.js';
 export * as jsonRpcClient from './json-rpc/client/index.js';
diff --git a/yarn-project/foundation/src/fifo/memory_fifo.ts b/yarn-project/foundation/src/queue/base_memory_queue.ts
similarity index 90%
rename from yarn-project/foundation/src/fifo/memory_fifo.ts
rename to yarn-project/foundation/src/queue/base_memory_queue.ts
index d7ef956d869..4677aa8e0b3 100644
--- a/yarn-project/foundation/src/fifo/memory_fifo.ts
+++ b/yarn-project/foundation/src/queue/base_memory_queue.ts
@@ -1,18 +1,19 @@
 import { TimeoutError } from '../error/index.js';
 import { createDebugLogger } from '../log/index.js';
 
-/**
- * A simple fifo queue. It can grow unbounded. It can have multiple producers and consumers.
- * Putting an item onto the queue always succeeds, unless either end() or cancel() has been called in which case
- * the item being pushed is simply discarded.
- */
-export class MemoryFifo<T> {
+export abstract class BaseMemoryQueue<T> {
   private waiting: ((item: T | null) => void)[] = [];
-  private items: T[] = [];
   private flushing = false;
 
   constructor(private log = createDebugLogger('aztec:foundation:memory_fifo')) {}
 
+  protected abstract get items(): {
+    length: number;
+    get(): T | undefined;
+    put(item: T): void;
+    clear: () => void;
+  };
+
   /**
    * Returns the current number of items in the queue.
    * The length represents the size of the queue at the time of invocation and may change as new items are added or consumed.
@@ -36,7 +37,7 @@ export class MemoryFifo<T> {
    */
   public get(timeoutSec?: number): Promise<T | null> {
     if (this.items.length) {
-      return Promise.resolve(this.items.shift()!);
+      return Promise.resolve(this.items.get()!);
     }
 
     if (this.items.length === 0 && this.flushing) {
@@ -78,7 +79,7 @@ export class MemoryFifo<T> {
       this.waiting.shift()!(item);
       return true;
     } else {
-      this.items.push(item);
+      this.items.put(item);
       return true;
     }
   }
@@ -100,7 +101,7 @@ export class MemoryFifo<T> {
    */
   public cancel() {
     this.flushing = true;
-    this.items = [];
+    this.items.clear();
     this.waiting.forEach(resolve => resolve(null));
   }
 
diff --git a/yarn-project/foundation/src/fifo/bounded_serial_queue.ts b/yarn-project/foundation/src/queue/bounded_serial_queue.ts
similarity index 100%
rename from yarn-project/foundation/src/fifo/bounded_serial_queue.ts
rename to yarn-project/foundation/src/queue/bounded_serial_queue.ts
diff --git a/yarn-project/foundation/src/queue/fifo_memory_queue.ts b/yarn-project/foundation/src/queue/fifo_memory_queue.ts
new file mode 100644
index 00000000000..e2271143ac6
--- /dev/null
+++ b/yarn-project/foundation/src/queue/fifo_memory_queue.ts
@@ -0,0 +1,39 @@
+import { type DebugLogger } from '../log/logger.js';
+import { BaseMemoryQueue } from './base_memory_queue.js';
+
+/**
+ * A simple fifo queue. It can grow unbounded. It can have multiple producers and consumers.
+ * Putting an item onto the queue always succeeds, unless either end() or cancel() has been called in which case
+ * the item being pushed is simply discarded.
+ */
+export class FifoMemoryQueue<T> extends BaseMemoryQueue<T> {
+  private container = new FifoQueue<T>();
+
+  constructor(log?: DebugLogger) {
+    super(log);
+  }
+
+  protected override get items() {
+    return this.container;
+  }
+}
+
+class FifoQueue<T> {
+  private items: T[] = [];
+
+  public put(item: T): void {
+    this.items.push(item);
+  }
+
+  public get(): T | undefined {
+    return this.items.shift();
+  }
+
+  public get length(): number {
+    return this.items.length;
+  }
+
+  public clear() {
+    this.items = [];
+  }
+}
diff --git a/yarn-project/foundation/src/fifo/index.ts b/yarn-project/foundation/src/queue/index.ts
similarity index 56%
rename from yarn-project/foundation/src/fifo/index.ts
rename to yarn-project/foundation/src/queue/index.ts
index 73b23f23dbd..e018dc2c2d3 100644
--- a/yarn-project/foundation/src/fifo/index.ts
+++ b/yarn-project/foundation/src/queue/index.ts
@@ -1,4 +1,5 @@
-export * from './memory_fifo.js';
+export * from './fifo_memory_queue.js';
+export * from './priority_memory_queue.js';
 export * from './serial_queue.js';
 export * from './bounded_serial_queue.js';
 export * from './semaphore.js';
diff --git a/yarn-project/foundation/src/queue/priority_memory_queue.test.ts b/yarn-project/foundation/src/queue/priority_memory_queue.test.ts
new file mode 100644
index 00000000000..e8b3f9b5ce2
--- /dev/null
+++ b/yarn-project/foundation/src/queue/priority_memory_queue.test.ts
@@ -0,0 +1,25 @@
+import { PriorityMemoryQueue } from './priority_memory_queue.js';
+
+describe('PriorityMemoryQueue', () => {
+  let queue: PriorityMemoryQueue<number>;
+
+  beforeEach(() => {
+    queue = new PriorityMemoryQueue<number>((a, b) => a - b);
+  });
+
+  it('returns items in the correct order', async () => {
+    expect(queue.put(3)).toBeTruthy();
+    expect(queue.put(1)).toBeTruthy();
+    expect(queue.put(2)).toBeTruthy();
+
+    expect(queue.length()).toEqual(3);
+
+    expect(await queue.get()).toBe(1);
+    expect(await queue.get()).toBe(2);
+    expect(await queue.get()).toBe(3);
+
+    expect(queue.length()).toEqual(0);
+
+    await expect(queue.get(1)).rejects.toThrow(/timeout/i);
+  });
+});
diff --git a/yarn-project/foundation/src/queue/priority_memory_queue.ts b/yarn-project/foundation/src/queue/priority_memory_queue.ts
new file mode 100644
index 00000000000..9dd3fe8ae46
--- /dev/null
+++ b/yarn-project/foundation/src/queue/priority_memory_queue.ts
@@ -0,0 +1,20 @@
+import { BaseMemoryQueue } from './base_memory_queue.js';
+import { PriorityQueue } from './priority_queue.js';
+
+/**
+ * A priority queue. It can grow unbounded. It can have multiple producers and consumers.
+ * Putting an item onto the queue always succeeds, unless either end() or cancel() has been called in which case
+ * the item being pushed is simply discarded.
+ */
+export class PriorityMemoryQueue<T> extends BaseMemoryQueue<T> {
+  private container: PriorityQueue<T>;
+
+  constructor(comparator: (a: T, b: T) => number) {
+    super();
+    this.container = new PriorityQueue(comparator);
+  }
+
+  protected override get items() {
+    return this.container;
+  }
+}
diff --git a/yarn-project/foundation/src/queue/priority_queue.ts b/yarn-project/foundation/src/queue/priority_queue.ts
new file mode 100644
index 00000000000..3da3feff66d
--- /dev/null
+++ b/yarn-project/foundation/src/queue/priority_queue.ts
@@ -0,0 +1,34 @@
+/**
+ * Priority queue implementation based on a custom comparator.
+ */
+export class PriorityQueue<T> {
+  private items: T[];
+
+  constructor(private comparator: (a: T, b: T) => number) {
+    this.items = [];
+  }
+
+  public put(item: T): void {
+    let i = 0;
+    while (i < this.items.length && this.comparator(item, this.items[i]) >= 0) {
+      i++;
+    }
+    this.items.splice(i, 0, item);
+  }
+
+  public get(): T | undefined {
+    return this.items.shift();
+  }
+
+  public peek(): T | undefined {
+    return this.items[0];
+  }
+
+  public clear() {
+    this.items = [];
+  }
+
+  public get length(): number {
+    return this.items.length;
+  }
+}
diff --git a/yarn-project/foundation/src/fifo/semaphore.ts b/yarn-project/foundation/src/queue/semaphore.ts
similarity index 90%
rename from yarn-project/foundation/src/fifo/semaphore.ts
rename to yarn-project/foundation/src/queue/semaphore.ts
index b1d17734049..d20bd9c4cd2 100644
--- a/yarn-project/foundation/src/fifo/semaphore.ts
+++ b/yarn-project/foundation/src/queue/semaphore.ts
@@ -1,10 +1,10 @@
-import { MemoryFifo } from './memory_fifo.js';
+import { FifoMemoryQueue } from './fifo_memory_queue.js';
 
 /**
  * Allows the acquiring of up to `size` tokens before calls to acquire block, waiting for a call to release().
  */
 export class Semaphore {
-  private readonly queue = new MemoryFifo<boolean>();
+  private readonly queue = new FifoMemoryQueue<boolean>();
 
   constructor(size: number) {
     new Array(size).fill(true).map(() => this.queue.put(true));
diff --git a/yarn-project/foundation/src/fifo/serial_queue.ts b/yarn-project/foundation/src/queue/serial_queue.ts
similarity index 95%
rename from yarn-project/foundation/src/fifo/serial_queue.ts
rename to yarn-project/foundation/src/queue/serial_queue.ts
index 6854cdc6ddc..b6bcd9baadd 100644
--- a/yarn-project/foundation/src/fifo/serial_queue.ts
+++ b/yarn-project/foundation/src/queue/serial_queue.ts
@@ -1,10 +1,10 @@
-import { MemoryFifo } from './memory_fifo.js';
+import { FifoMemoryQueue } from './fifo_memory_queue.js';
 
 /**
  * A more specialized fifo queue that enqueues functions to execute. Enqueued functions are executed in serial.
  */
 export class SerialQueue {
-  private readonly queue = new MemoryFifo<() => Promise<void>>();
+  private readonly queue = new FifoMemoryQueue<() => Promise<void>>();
   private runningPromise!: Promise<void>;
 
   /**
diff --git a/yarn-project/foundation/src/wasm/wasm_module.ts b/yarn-project/foundation/src/wasm/wasm_module.ts
index 20851a05cc6..f0c3a15debe 100644
--- a/yarn-project/foundation/src/wasm/wasm_module.ts
+++ b/yarn-project/foundation/src/wasm/wasm_module.ts
@@ -1,8 +1,8 @@
 import { Buffer } from 'buffer';
 
 import { randomBytes } from '../crypto/index.js';
-import { MemoryFifo } from '../fifo/index.js';
 import { type LogFn, createDebugOnlyLogger } from '../log/index.js';
+import { FifoMemoryQueue } from '../queue/index.js';
 import { getEmptyWasiSdk } from './empty_wasi_sdk.js';
 
 /**
@@ -47,7 +47,7 @@ export class WasmModule implements IWasmModule {
   private memory!: WebAssembly.Memory;
   private heap!: Uint8Array;
   private instance?: WebAssembly.Instance;
-  private mutexQ = new MemoryFifo<boolean>();
+  private mutexQ = new FifoMemoryQueue<boolean>();
   private debug: LogFn;
 
   /**
diff --git a/yarn-project/p2p/src/service/libp2p_service.ts b/yarn-project/p2p/src/service/libp2p_service.ts
index 6f8d9d9d234..4570c8291f5 100644
--- a/yarn-project/p2p/src/service/libp2p_service.ts
+++ b/yarn-project/p2p/src/service/libp2p_service.ts
@@ -1,6 +1,6 @@
 import { type Gossipable, type RawGossipMessage, TopicType, TopicTypeMap, Tx } from '@aztec/circuit-types';
-import { SerialQueue } from '@aztec/foundation/fifo';
 import { createDebugLogger } from '@aztec/foundation/log';
+import { SerialQueue } from '@aztec/foundation/queue';
 import { RunningPromise } from '@aztec/foundation/running-promise';
 import type { AztecKVStore } from '@aztec/kv-store';
 
diff --git a/yarn-project/prover-client/src/orchestrator/orchestrator.ts b/yarn-project/prover-client/src/orchestrator/orchestrator.ts
index 1a8f795b39e..ae00044dcda 100644
--- a/yarn-project/prover-client/src/orchestrator/orchestrator.ts
+++ b/yarn-project/prover-client/src/orchestrator/orchestrator.ts
@@ -345,6 +345,7 @@ export class ProvingOrchestrator implements BlockProver {
               getVKTreeRoot(),
             ),
             signal,
+            provingState.epochNumber,
           ),
       ),
       result => {
@@ -577,7 +578,7 @@ export class ProvingOrchestrator implements BlockProver {
       return;
     }
 
-    // We build tha base rollup inputs using a mock proof and verification key.
+    // We build the base rollup inputs using a mock proof and verification key.
     // These will be overwritten later once we have proven the tube circuit and any public kernels
     const [ms, inputs] = await elapsed(
       buildBaseRollupInput(
@@ -697,7 +698,7 @@ export class ProvingOrchestrator implements BlockProver {
           [Attributes.PROTOCOL_CIRCUIT_TYPE]: 'server',
           [Attributes.PROTOCOL_CIRCUIT_NAME]: 'base-rollup' as CircuitName,
         },
-        signal => this.prover.getBaseRollupProof(tx.baseRollupInputs, signal),
+        signal => this.prover.getBaseRollupProof(tx.baseRollupInputs, signal, provingState.epochNumber),
       ),
       result => {
         logger.debug(`Completed proof for base rollup for tx ${tx.processedTx.hash.toString()}`);
@@ -733,7 +734,12 @@ export class ProvingOrchestrator implements BlockProver {
           [Attributes.PROTOCOL_CIRCUIT_TYPE]: 'server',
           [Attributes.PROTOCOL_CIRCUIT_NAME]: 'tube-circuit' as CircuitName,
         },
-        signal => this.prover.getTubeProof(new TubeInputs(txProvingState.processedTx.clientIvcProof), signal),
+        signal =>
+          this.prover.getTubeProof(
+            new TubeInputs(txProvingState.processedTx.clientIvcProof),
+            signal,
+            provingState.epochNumber,
+          ),
       ),
       result => {
         logger.debug(`Completed tube proof for tx index: ${txIndex}`);
@@ -772,7 +778,7 @@ export class ProvingOrchestrator implements BlockProver {
           [Attributes.PROTOCOL_CIRCUIT_TYPE]: 'server',
           [Attributes.PROTOCOL_CIRCUIT_NAME]: 'merge-rollup' as CircuitName,
         },
-        signal => this.prover.getMergeRollupProof(inputs, signal),
+        signal => this.prover.getMergeRollupProof(inputs, signal, provingState.epochNumber),
       ),
       result => {
         this.storeAndExecuteNextMergeLevel(provingState, level, index, [
@@ -817,7 +823,7 @@ export class ProvingOrchestrator implements BlockProver {
           [Attributes.PROTOCOL_CIRCUIT_TYPE]: 'server',
           [Attributes.PROTOCOL_CIRCUIT_NAME]: 'root-rollup' as CircuitName,
         },
-        signal => this.prover.getRootRollupProof(inputs, signal),
+        signal => this.prover.getRootRollupProof(inputs, signal, provingState.epochNumber),
       ),
       result => {
         provingState.rootRollupPublicInputs = result.inputs;
@@ -847,7 +853,7 @@ export class ProvingOrchestrator implements BlockProver {
           [Attributes.PROTOCOL_CIRCUIT_TYPE]: 'server',
           [Attributes.PROTOCOL_CIRCUIT_NAME]: 'base-parity' as CircuitName,
         },
-        signal => this.prover.getBaseParityProof(inputs, signal),
+        signal => this.prover.getBaseParityProof(inputs, signal, provingState.epochNumber),
       ),
       rootInput => {
         provingState.setRootParityInputs(rootInput, index);
@@ -866,7 +872,7 @@ export class ProvingOrchestrator implements BlockProver {
 
   // Runs the root parity circuit ans stored the outputs
   // Enqueues the root rollup proof if all inputs are available
-  private enqueueRootParityCircuit(provingState: ProvingState | undefined, inputs: RootParityInputs) {
+  private enqueueRootParityCircuit(provingState: ProvingState, inputs: RootParityInputs) {
     this.deferredProving(
       provingState,
       wrapCallbackInSpan(
@@ -876,7 +882,7 @@ export class ProvingOrchestrator implements BlockProver {
           [Attributes.PROTOCOL_CIRCUIT_TYPE]: 'server',
           [Attributes.PROTOCOL_CIRCUIT_NAME]: 'root-parity' as CircuitName,
         },
-        signal => this.prover.getRootParityProof(inputs, signal),
+        signal => this.prover.getRootParityProof(inputs, signal, provingState.epochNumber),
       ),
       async rootInput => {
         provingState!.finalRootParityInput = rootInput;
@@ -962,7 +968,7 @@ export class ProvingOrchestrator implements BlockProver {
             publicFunction.vmRequest!.avmHints,
           );
           try {
-            return await this.prover.getAvmProof(inputs, signal);
+            return await this.prover.getAvmProof(inputs, signal, provingState.epochNumber);
           } catch (err) {
             if (process.env.AVM_PROVING_STRICT) {
               throw err;
@@ -1073,9 +1079,9 @@ export class ProvingOrchestrator implements BlockProver {
           signal,
         ): Promise<PublicInputsAndRecursiveProof<KernelCircuitPublicInputs | PublicKernelCircuitPublicInputs>> => {
           if (request.type === PublicKernelType.TAIL) {
-            return this.prover.getPublicTailProof(request, signal);
+            return this.prover.getPublicTailProof(request, signal, provingState.epochNumber);
           } else {
-            return this.prover.getPublicKernelProof(request, signal);
+            return this.prover.getPublicKernelProof(request, signal, provingState.epochNumber);
           }
         },
       ),
diff --git a/yarn-project/prover-client/src/orchestrator/proving-state.ts b/yarn-project/prover-client/src/orchestrator/proving-state.ts
index e247b6f0d20..b375bb7e0ac 100644
--- a/yarn-project/prover-client/src/orchestrator/proving-state.ts
+++ b/yarn-project/prover-client/src/orchestrator/proving-state.ts
@@ -143,6 +143,11 @@ export class ProvingState {
     return this.txs;
   }
 
+  /** Returns the block number as an epoch number. Used for prioritizing proof requests. */
+  public get epochNumber(): number {
+    return this.globalVariables.blockNumber.toNumber();
+  }
+
   /**
    * Stores the inputs to a merge circuit and determines if the circuit is ready to be executed
    * @param mergeInputs - The inputs to store
diff --git a/yarn-project/prover-client/src/prover-agent/memory-proving-queue.test.ts b/yarn-project/prover-client/src/prover-agent/memory-proving-queue.test.ts
index 41eb09a9e54..a581c4012d0 100644
--- a/yarn-project/prover-client/src/prover-agent/memory-proving-queue.test.ts
+++ b/yarn-project/prover-client/src/prover-agent/memory-proving-queue.test.ts
@@ -7,7 +7,12 @@ import {
   VerificationKeyAsFields,
   makeRecursiveProof,
 } from '@aztec/circuits.js';
-import { makeBaseParityInputs, makeBaseRollupInputs, makeParityPublicInputs } from '@aztec/circuits.js/testing';
+import {
+  makeBaseParityInputs,
+  makeBaseRollupInputs,
+  makeParityPublicInputs,
+  makeRootRollupInputs,
+} from '@aztec/circuits.js/testing';
 import { makeTuple } from '@aztec/foundation/array';
 import { AbortError } from '@aztec/foundation/error';
 import { sleep } from '@aztec/foundation/sleep';
@@ -42,6 +47,32 @@ describe('MemoryProvingQueue', () => {
     expect(job2?.request.type).toEqual(ProvingRequestType.BASE_ROLLUP);
   });
 
+  it('returns jobs ordered by priority', async () => {
+    // We push base rollup proof requests for a first block
+    void queue.getBaseRollupProof(makeBaseRollupInputs(), undefined, 1);
+    void queue.getBaseRollupProof(makeBaseRollupInputs(), undefined, 1);
+
+    // The agent consumes one of them
+    expect((await queue.getProvingJob())!.request.type).toEqual(ProvingRequestType.BASE_ROLLUP);
+
+    // A new block comes along with its base rollups, and the orchestrator then pushes a root request for the first one
+    void queue.getBaseRollupProof(makeBaseRollupInputs(), undefined, 2);
+    void queue.getBaseRollupProof(makeBaseRollupInputs(), undefined, 2);
+    void queue.getBaseRollupProof(makeBaseRollupInputs(), undefined, 2);
+    void queue.getBaseRollupProof(makeBaseRollupInputs(), undefined, 2);
+    void queue.getRootRollupProof(makeRootRollupInputs(), undefined, 1);
+
+    // The next jobs for the agent should be the ones from block 1, skipping the ones for block 2
+    expect((await queue.getProvingJob())!.request.type).toEqual(ProvingRequestType.BASE_ROLLUP);
+    expect((await queue.getProvingJob())!.request.type).toEqual(ProvingRequestType.ROOT_ROLLUP);
+
+    // And the base rollups for block 2 should go next
+    expect((await queue.getProvingJob())!.request.type).toEqual(ProvingRequestType.BASE_ROLLUP);
+    expect((await queue.getProvingJob())!.request.type).toEqual(ProvingRequestType.BASE_ROLLUP);
+    expect((await queue.getProvingJob())!.request.type).toEqual(ProvingRequestType.BASE_ROLLUP);
+    expect((await queue.getProvingJob())!.request.type).toEqual(ProvingRequestType.BASE_ROLLUP);
+  });
+
   it('returns undefined when no jobs are available', async () => {
     await expect(queue.getProvingJob({ timeoutSec: 0 })).resolves.toBeUndefined();
   });
diff --git a/yarn-project/prover-client/src/prover-agent/memory-proving-queue.ts b/yarn-project/prover-client/src/prover-agent/memory-proving-queue.ts
index 0ee31b82acc..a161722315b 100644
--- a/yarn-project/prover-client/src/prover-agent/memory-proving-queue.ts
+++ b/yarn-project/prover-client/src/prover-agent/memory-proving-queue.ts
@@ -31,34 +31,35 @@ import type {
 } from '@aztec/circuits.js';
 import { randomBytes } from '@aztec/foundation/crypto';
 import { AbortError, TimeoutError } from '@aztec/foundation/error';
-import { MemoryFifo } from '@aztec/foundation/fifo';
 import { createDebugLogger } from '@aztec/foundation/log';
 import { type PromiseWithResolvers, RunningPromise, promiseWithResolvers } from '@aztec/foundation/promise';
+import { PriorityMemoryQueue } from '@aztec/foundation/queue';
 import { serializeToBuffer } from '@aztec/foundation/serialize';
 import { type TelemetryClient } from '@aztec/telemetry-client';
 
 import { ProvingQueueMetrics } from './queue_metrics.js';
 
-type ProvingJobWithResolvers<T extends ProvingRequest = ProvingRequest> = {
-  id: string;
-  request: T;
-  signal?: AbortSignal;
-  attempts: number;
-  heartbeat: number;
-} & PromiseWithResolvers<ProvingRequestResult<T['type']>>;
+type ProvingJobWithResolvers<T extends ProvingRequest = ProvingRequest> = ProvingJob<T> &
+  PromiseWithResolvers<ProvingRequestResult<T['type']>> & {
+    signal?: AbortSignal;
+    epochNumber?: number;
+    attempts: number;
+    heartbeat: number;
+  };
 
 const MAX_RETRIES = 3;
 
 const defaultIdGenerator = () => randomBytes(4).toString('hex');
 const defaultTimeSource = () => Date.now();
-
 /**
  * A helper class that sits in between services that need proofs created and agents that can create them.
- * The queue accumulates jobs and provides them to agents in FIFO order.
+ * The queue accumulates jobs and provides them to agents prioritized by block number.
  */
 export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource {
   private log = createDebugLogger('aztec:prover-client:prover-pool:queue');
-  private queue = new MemoryFifo<ProvingJobWithResolvers>();
+  private queue = new PriorityMemoryQueue<ProvingJobWithResolvers>(
+    (a, b) => (a.epochNumber ?? 0) - (b.epochNumber ?? 0),
+  );
   private jobsInProgress = new Map<string, ProvingJobWithResolvers>();
 
   private runningPromise: RunningPromise;
@@ -220,6 +221,7 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   private enqueue<T extends ProvingRequest>(
     request: T,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<ProvingRequestResult<T['type']>> {
     if (!this.runningPromise.isRunning()) {
       return Promise.reject(new Error('Proving queue is not running.'));
@@ -235,6 +237,7 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
       reject,
       attempts: 1,
       heartbeat: 0,
+      epochNumber,
     };
 
     if (signal) {
@@ -258,22 +261,25 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getEmptyPrivateKernelProof(
     inputs: PrivateKernelEmptyInputData,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<KernelCircuitPublicInputs>> {
-    return this.enqueue({ type: ProvingRequestType.PRIVATE_KERNEL_EMPTY, inputs }, signal);
+    return this.enqueue({ type: ProvingRequestType.PRIVATE_KERNEL_EMPTY, inputs }, signal, epochNumber);
   }
 
   getTubeProof(
     inputs: TubeInputs,
-    signal?: AbortSignal | undefined,
+    signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<{ tubeVK: VerificationKeyData; tubeProof: RecursiveProof<typeof RECURSIVE_PROOF_LENGTH> }> {
-    return this.enqueue({ type: ProvingRequestType.TUBE_PROOF, inputs }, signal);
+    return this.enqueue({ type: ProvingRequestType.TUBE_PROOF, inputs }, signal, epochNumber);
   }
 
   getEmptyTubeProof(
     inputs: PrivateKernelEmptyInputData,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<KernelCircuitPublicInputs>> {
-    return this.enqueue({ type: ProvingRequestType.PRIVATE_KERNEL_EMPTY, inputs }, signal);
+    return this.enqueue({ type: ProvingRequestType.PRIVATE_KERNEL_EMPTY, inputs }, signal, epochNumber);
   }
 
   /**
@@ -283,14 +289,9 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getBaseParityProof(
     inputs: BaseParityInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<RootParityInput<typeof RECURSIVE_PROOF_LENGTH>> {
-    return this.enqueue(
-      {
-        type: ProvingRequestType.BASE_PARITY,
-        inputs,
-      },
-      signal,
-    );
+    return this.enqueue({ type: ProvingRequestType.BASE_PARITY, inputs }, signal, epochNumber);
   }
 
   /**
@@ -300,14 +301,9 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getRootParityProof(
     inputs: RootParityInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<RootParityInput<typeof NESTED_RECURSIVE_PROOF_LENGTH>> {
-    return this.enqueue(
-      {
-        type: ProvingRequestType.ROOT_PARITY,
-        inputs,
-      },
-      signal,
-    );
+    return this.enqueue({ type: ProvingRequestType.ROOT_PARITY, inputs }, signal, epochNumber);
   }
 
   /**
@@ -317,14 +313,9 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getBaseRollupProof(
     baseRollupInput: BaseRollupInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<BaseOrMergeRollupPublicInputs>> {
-    return this.enqueue(
-      {
-        type: ProvingRequestType.BASE_ROLLUP,
-        inputs: baseRollupInput,
-      },
-      signal,
-    );
+    return this.enqueue({ type: ProvingRequestType.BASE_ROLLUP, inputs: baseRollupInput }, signal, epochNumber);
   }
 
   /**
@@ -334,14 +325,9 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getMergeRollupProof(
     input: MergeRollupInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<BaseOrMergeRollupPublicInputs>> {
-    return this.enqueue(
-      {
-        type: ProvingRequestType.MERGE_ROLLUP,
-        inputs: input,
-      },
-      signal,
-    );
+    return this.enqueue({ type: ProvingRequestType.MERGE_ROLLUP, inputs: input }, signal, epochNumber);
   }
 
   /**
@@ -351,14 +337,9 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getRootRollupProof(
     input: RootRollupInputs,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<RootRollupPublicInputs>> {
-    return this.enqueue(
-      {
-        type: ProvingRequestType.ROOT_ROLLUP,
-        inputs: input,
-      },
-      signal,
-    );
+    return this.enqueue({ type: ProvingRequestType.ROOT_ROLLUP, inputs: input }, signal, epochNumber);
   }
 
   /**
@@ -368,14 +349,12 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getPublicKernelProof(
     kernelRequest: PublicKernelNonTailRequest,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<PublicKernelCircuitPublicInputs>> {
     return this.enqueue(
-      {
-        type: ProvingRequestType.PUBLIC_KERNEL_NON_TAIL,
-        kernelType: kernelRequest.type,
-        inputs: kernelRequest.inputs,
-      },
+      { type: ProvingRequestType.PUBLIC_KERNEL_NON_TAIL, kernelType: kernelRequest.type, inputs: kernelRequest.inputs },
       signal,
+      epochNumber,
     );
   }
 
@@ -386,28 +365,20 @@ export class MemoryProvingQueue implements ServerCircuitProver, ProvingJobSource
   getPublicTailProof(
     kernelRequest: PublicKernelTailRequest,
     signal?: AbortSignal,
+    epochNumber?: number,
   ): Promise<PublicInputsAndRecursiveProof<KernelCircuitPublicInputs>> {
     return this.enqueue(
-      {
-        type: ProvingRequestType.PUBLIC_KERNEL_TAIL,
-        kernelType: kernelRequest.type,
-        inputs: kernelRequest.inputs,
-      },
+      { type: ProvingRequestType.PUBLIC_KERNEL_TAIL, kernelType: kernelRequest.type, inputs: kernelRequest.inputs },
       signal,
+      epochNumber,
     );
   }
 
   /**
    * Creates an AVM proof.
    */
-  getAvmProof(inputs: AvmCircuitInputs, signal?: AbortSignal | undefined): Promise<ProofAndVerificationKey> {
-    return this.enqueue(
-      {
-        type: ProvingRequestType.PUBLIC_VM,
-        inputs,
-      },
-      signal,
-    );
+  getAvmProof(inputs: AvmCircuitInputs, signal?: AbortSignal, epochNumber?: number): Promise<ProofAndVerificationKey> {
+    return this.enqueue({ type: ProvingRequestType.PUBLIC_VM, inputs }, signal, epochNumber);
   }
 
   /**
diff --git a/yarn-project/pxe/src/pxe_service/pxe_service.ts b/yarn-project/pxe/src/pxe_service/pxe_service.ts
index 1b8708d9582..7b6ba12d62c 100644
--- a/yarn-project/pxe/src/pxe_service/pxe_service.ts
+++ b/yarn-project/pxe/src/pxe_service/pxe_service.ts
@@ -44,8 +44,8 @@ import {
   encodeArguments,
 } from '@aztec/foundation/abi';
 import { type Fq, Fr, type Point } from '@aztec/foundation/fields';
-import { SerialQueue } from '@aztec/foundation/fifo';
 import { type DebugLogger, createDebugLogger } from '@aztec/foundation/log';
+import { SerialQueue } from '@aztec/foundation/queue';
 import { type KeyStore } from '@aztec/key-store';
 import { ClassRegistererAddress } from '@aztec/protocol-contracts/class-registerer';
 import { getCanonicalFeeJuice } from '@aztec/protocol-contracts/fee-juice';
diff --git a/yarn-project/pxe/src/synchronizer/synchronizer.test.ts b/yarn-project/pxe/src/synchronizer/synchronizer.test.ts
index 6a55b6cb052..ea2d1d86c39 100644
--- a/yarn-project/pxe/src/synchronizer/synchronizer.test.ts
+++ b/yarn-project/pxe/src/synchronizer/synchronizer.test.ts
@@ -2,7 +2,7 @@ import { type AztecNode, L2Block } from '@aztec/circuit-types';
 import { Fr, type Header, INITIAL_L2_BLOCK_NUM } from '@aztec/circuits.js';
 import { makeHeader } from '@aztec/circuits.js/testing';
 import { randomInt } from '@aztec/foundation/crypto';
-import { SerialQueue } from '@aztec/foundation/fifo';
+import { SerialQueue } from '@aztec/foundation/queue';
 import { KeyStore } from '@aztec/key-store';
 import { openTmpStore } from '@aztec/kv-store/utils';
 
diff --git a/yarn-project/pxe/src/synchronizer/synchronizer.ts b/yarn-project/pxe/src/synchronizer/synchronizer.ts
index 52d7cc3d3a4..0ddfcc191aa 100644
--- a/yarn-project/pxe/src/synchronizer/synchronizer.ts
+++ b/yarn-project/pxe/src/synchronizer/synchronizer.ts
@@ -1,8 +1,8 @@
 import { type AztecNode, type L2Block, MerkleTreeId, type TxHash } from '@aztec/circuit-types';
 import { type NoteProcessorCaughtUpStats } from '@aztec/circuit-types/stats';
 import { type AztecAddress, type Fr, INITIAL_L2_BLOCK_NUM, type PublicKey } from '@aztec/circuits.js';
-import { type SerialQueue } from '@aztec/foundation/fifo';
 import { type DebugLogger, createDebugLogger } from '@aztec/foundation/log';
+import { type SerialQueue } from '@aztec/foundation/queue';
 import { RunningPromise } from '@aztec/foundation/running-promise';
 import { type KeyStore } from '@aztec/key-store';
 
diff --git a/yarn-project/world-state/src/synchronizer/server_world_state_synchronizer.ts b/yarn-project/world-state/src/synchronizer/server_world_state_synchronizer.ts
index fd99f6ba9ce..a4512b41048 100644
--- a/yarn-project/world-state/src/synchronizer/server_world_state_synchronizer.ts
+++ b/yarn-project/world-state/src/synchronizer/server_world_state_synchronizer.ts
@@ -8,9 +8,9 @@ import {
 import { type L2BlockHandledStats } from '@aztec/circuit-types/stats';
 import { L1_TO_L2_MSG_SUBTREE_HEIGHT } from '@aztec/circuits.js/constants';
 import { Fr } from '@aztec/foundation/fields';
-import { SerialQueue } from '@aztec/foundation/fifo';
 import { createDebugLogger } from '@aztec/foundation/log';
 import { promiseWithResolvers } from '@aztec/foundation/promise';
+import { SerialQueue } from '@aztec/foundation/queue';
 import { elapsed } from '@aztec/foundation/timer';
 import { type AztecKVStore, type AztecSingleton } from '@aztec/kv-store';
 import { openTmpStore } from '@aztec/kv-store/utils';
diff --git a/yarn-project/world-state/src/world-state-db/merkle_trees.ts b/yarn-project/world-state/src/world-state-db/merkle_trees.ts
index 0ebd9937bca..8db05dc8119 100644
--- a/yarn-project/world-state/src/world-state-db/merkle_trees.ts
+++ b/yarn-project/world-state/src/world-state-db/merkle_trees.ts
@@ -30,8 +30,8 @@ import {
   StateReference,
 } from '@aztec/circuits.js';
 import { padArrayEnd } from '@aztec/foundation/collection';
-import { SerialQueue } from '@aztec/foundation/fifo';
 import { type DebugLogger, createDebugLogger } from '@aztec/foundation/log';
+import { SerialQueue } from '@aztec/foundation/queue';
 import { type IndexedTreeLeafPreimage } from '@aztec/foundation/trees';
 import { type AztecKVStore, type AztecSingleton } from '@aztec/kv-store';
 import {