FastAPI request don't execute in parallel

Question

I'm working on OpenAI chatbot and this is FastAPI backend code.

from fastapi import FastAPI, Response
from fastapi.middleware.cors import CORSMiddleware
from dotenv import load_dotenv
from pydantic import BaseModel
from langchain.callbacks import AsyncIteratorCallbackHandler
from typing import AsyncIterable, Awaitable
from fastapi.responses import StreamingResponse
import openai
import os
import uuid
import asyncio

load_dotenv()

openai.api_key = os.getenv("OPENAI_API_KEY")

app = FastAPI()
app.add_middleware(CORSMiddleware, allow_origins=[
                   "*"], allow_credentials=True, allow_methods=["*"], allow_headers=["*"])

messages = {}
subject = "wine"
instructor = f"""You're a assistant helping humans. Please answer questions as detail as possible.
                And please format them in a user-friendly way, easy to read.
                If human's asking about something that is not related with ${subject}, just tell him you only answer about ${subject}.
            """
remember_cnt = 10


def initializeMemory(token: str):
    global messages
    messages[token] = []


class Message(BaseModel):
    message: str
    token: str


class Token(BaseModel):
    token: str


async def send_message(message: str, token: str) -> AsyncIterable[str]:

    if (token not in messages):
        messages[token] = []
    messages[token].append({'role': 'user', 'content': message})
    response = openai.ChatCompletion.create(
        model='gpt-4',
        messages=[{'role': 'system', 'content': instructor}] +
        messages[token][-remember_cnt:],
        temperature=0,
        stream=True
    )

    final = ""
    for chunk in response:
        if 'content' in chunk.choices[0].delta:
            string = chunk.choices[0].delta.content
            final += string
            if string.isspace() and len(string.strip()) == 0:
                yield '\n'
            else:
                yield string

    messages[token].append({'role': 'assistant', 'content': final})


@app.post("/memory-clear")
async def memory_clear(token: Token):
    if (token.token != ""):
        initializeMemory(token.token)
    if (token.token == ""):
        return uuid.uuid4()
    else:
        return ""

@app.post("/chat")
async def get_answer(message: Message):
    return StreamingResponse(send_message(message.message, message.token), media_type='text/event-stream')

if __name__ == "__main__":
    import uvicorn
    uvicorn.run(host="0.0.0.0", port=8080, app=app)

Everything's working fine. But the problem is when two users call /chat api at the same time, the don't execute in parallel. They executed one by one so second user have to wait until first user's request fulfilled. How Can I fix this?

I've heard we can use asyncio but I don't know how to use it.