As I see they are two independent methods, so there's no problem in parallelizing them. You could launch an executor service to do that and then await for termination:

    @Override 
    protected Integer doInBackground(Void... params) {
    	Integer result = null;
    	try{
    		ExecutorService executor = Executors.newFixedThreadPool(2);
    		Runnable thread1 = new Runnable() {
    			@Override
    			public void run() {
    				try {
    					method1(_phoneno);
    				} catch (Exception ex) {
    					throw new RuntimeException(ex);
    				}
    			}
    		};
    		executor.submit(thread1);
    		Runnable thread2 = new Runnable() {
    			@Override
    			public void run() {
    				try {
    					result = method2(_phoneno,_ticket);
    				} catch (Exception ex) {
    					throw new RuntimeException(ex);
    				}
    			}
    		};
    		executor.submit(thread2);
    		executor.shutdown();
    		//Timeout for both tasks = 120 seconds
    		if (!executor.awaitTermination(120, TimeUnit.SECONDS)){
    			throw new RuntimeException("Could not complete requests in the given time!");
    		}
    		return result;
    	}catch(Exception ex){
    		//Keep your exception to be shown in a toast
    		exception = ex;
    	}
    }

See also:

 - https://stackoverflow.com/questions/1250643/how-to-wait-for-all-threads-to-finish-using-executorservice