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Implement connection pooling with request pipelining for network services to optimize resource usage and improve throughput. Pool should manage three resource levels:

1. Channels (TCP connections): Share between multiple clients with HTTP/2 multiplexing
2. Clients: Acquire from channel pool, return when done
3. Streams: Reuse for multiple requests with controlled queue depth

Example implementation:

const CLIENTS_PER_CHANNEL: usize = 16;
const STREAM_QUEUE_DEPTH: usize = 2;

pub struct ChannelPool {
    channels: Mutex<BTreeMap<ChannelID, ChannelEntry>>,
}

pub struct ClientPool {
    channel_pool: Arc<ChannelPool>,
    idle: Mutex<BTreeMap<ClientID, ClientEntry>>,
}

pub struct StreamPool {
    client_pool: Arc<ClientPool>,
    streams: Arc<Mutex<HashMap<StreamID, StreamEntry>>>,
}

Key principles:

• Use HTTP/2 stream multiplexing to share TCP connections
• Pipeline multiple requests (queue depth 2-3) to mask network latency
• Return resources to pool promptly to enable reuse
• Implement proper backpressure through queue depth limits
• Consider cleanup of idle resources after timeout period